This should be kinda fun. I'll give you the biggest points.
If you know about all the expanding they did, then I'm sure you know about Vince owning WCW. Well with the roster being so big, it was decided that RAW and Smackdown! would each have their own separate rosters. This was done with a draft in March of 2002.
GENERAL MANAGERS/BOSSES
For a few months, Vince McMahon was in charge of Smackdown! while Ric Flair was in charge of RAW. That situation quickly fizzled away when Flair started hanging out with Triple H. So Vince then decided to assign General Managers to each show in July of 2002. He assigned Stephanie McMahon to run Smackdown! and former WCW president Eric Bischoff was put in charge of RAW.
Eric Bischoff immediately ran rampant on RAW being completely and utterly unfair. He favored all the heels and made the faces' lives a miserable hell. He's been a horrible general manager ever since then. In that time, he has been held in check a few times by the return of Stone Cold Steve Austin in February 2003 as a wrestler, the return of Austin in May 2003 as Co-GM, the return of Mick Foley as temporary Co-GM in November and December of 2003, and the return of Austin as RAW Sherriff in January 2004.
On Smackdown! however, there have been several General Managers. Nobody seems to be able to keep a job. Stephanie was the original and did a damn good job too. She was fair and unbiased and did what was good for the fans and for Smackdown!. For most of 2002, Smackdown! was hands down the best show on WWE television. But Vince McMahon drove her out of her job by forcing her to compete in an I Quit match at No Mercy 2003. Stephanie lost the match and her job. Vince then hired Paul Heyman as the General Manager. Heyman's rule was also vendictive and unfair, much like Bischoff's on RAW. Heyman's run as GM ended when he was drafted to RAW after this year's WrestleMania. He refused to work for Bischoff and quit. The vacant GM spot was filled by Kurt Angle, who was later injured by the Big Show and confined to a wheel chair. It was found out just weeks ago that Kurt Angle was never really injured and that he had been lying to everyone about his apparent injury. Kurt was also a ruthless and evil GM. Vince fired Kurt as GM and re-hired him as a wrestler. And just about 10 days ago, Vince hired Theodore R. Long (who you might know as a former referee) as the new General Manager of Smackdown!. So far, Theodore has run two episodes and has done a great job, signing quality matches for television and important title matches for SummerSlam.
JUMPING SHIP/ROSTER SPOTS
At the beginning of the brand extension, everybody was free to come and go as they pleased from either show. Many wrestlers jumped ship to go work for the other show. The biggest jump was probably Brock Lesnar, who went from RAW to Smackdown! and became highly successful as the youngest WWE Champion ever. Other big jumps were Undertaker to SD, Chris Jericho to RAW, and Triple H to RAW. Essentially, you wrestlers were under contract to a specific show. Only the Undisputed Heavyweight Champion and the Women's Champion could appear on both shows. Eventually, Vince McMahon stated that the rosters would be frozen and that nobody, including title holders, could leave a show unless their contract with that show expired or unless a trade was made.
VARIOUS BIG TIME STORIES
Triple H jumped to RAW in July of 2002 under the persuasion of his friend Shawn Michaels. On one episode of RAW, it appeared as if they were officially restarting Degeneration X. But during the celebration of their reunion, Triple H turned on Michaels and Pedigreed him in the middle of the ring. The next week, Michaels was assaulted in the parking lot and put out of action. It was later revealed that HHH was the attacker. They had a classic street fight at Summerslam that year. HBK won. Their feud continued off and on, sometimes with the Heavyweight Title on the line, and seems to have come to an end after their Hell in a Cell match in June 2004.
Brock Lesnar jumped from RAW to Smackdown! after King of the Ring 2002. At SummerSlam 2002, he defeated The Rock for the Undisputed Championship. After this happened, Vince froze the rosters. Smackdown! had control of the Undisputed Title.
In September of 2002, Eric Bischoff solved the problem on RAW by bringing back the World Title, the most recent Heavyweight belt from WCW (SD! officially brought back the WWE Title). Controversially, he awarded it to Triple H, no strings attached. Triple H held the title through a series of unfair wins and self-disqualifications for 11 out of the next 12 months.
Hulk Hogan came back as a part of the revived nWo. Vince brought them back to kill the WWE, since he thought Flair would end up destroying the company that Vince built. The nWo quickly died out. Scott Hall was fired. Kevin Nash was injured. But Hogan went on to win the WWE title on Smackdown!, holding it only for a month before losing it to The Undertaker. He had two brief feuds with The Rock, resulting in two PPV matches. One was at WrestleMania 2002 and it was historic to say the least. He was gone for a while toward the end of 2002, but came back in 2003. He was suspended, but came back wearing a mask and patriotic colors performing under the name Mr. America. He was fired for breaching his contract when Vince was finally able to catch Hogan unveiling his face on camera.
Ric Flair and Triple H formed a group with young superstars Randy Orton and Dave Batista, naming it Evolution. It is more or less a Four Horsemen rip off. But entertaining nonetheless. They formed in 2003 and have been running strong ever since. In December of 2003, they officially claimed dominance over RAW by taking posession of the World Heavyweight Title, the Intercontinental Title, and the WWE Tag Titles.
The U.S. Title was brought to Smackdown! as it's equivalent of RAW's Intercontinental Title.
By the way, Bischoff made some stupid moves as GM. He abolished the Intercontinental, European and Hardcore Titles, merging them all together, and then merging that with the World Title to try to make that title "more prestigious." But this left most of the RAW roster with nothing to fight for. RAW became ridiculous and almost completely frustrating to watch. When Austin returned as Co-GM, he brought back the IC belt.
Goldberg joined the WWE in March 2003. He stayed one year. In that time he had a big feud with Triple H, winning the World Title and keeping it for a couple months. He then feuded with Brock Lesnar and faced him at WrestleMania XX. This was an interpromotional match as Goldberg was on RAW and Lesnar on Smackdown!.
Possibly the biggest story was the unmasking of Kane. In summer of 2003, Kane had been out of his shell for a while. He tagged for a while with Rob Van Dam and even became Tag Champions with him. He started joking around and doing silly moves and impersonations with RVD. He even once did the Kane-A-Roonie, a horrible attempt at the Spin-A-Roonie. Austin eventually called out Kane and lambasted him for having "gone soft," something that many fans were also thinking but couldn't say on television of course. Austin stunned Kane and started to bring back some of the fire. He gave Kane the opportunity to wrestle Triple H for the World Title on RAW. But Eric Bischoff put in a stipulation that said Kane would have to unmask if he didn't win the belt. Kane agreed. He lost the match and unmasked at the end of RAW in June of 2003. Without the mask, Kane became more of a monster than ever before, enraged by the thought of people making fun of his "deformed" face. In an interview with Jim Ross, J.R. pointed out that Kane's face did not look scarred or twisted at all, suggesting that Kane's deformities may only be in his mind. Kane became enraged and set J.R. on fire. Other hideous acts included chokeslamming Bischoff off the RAW stage and through a table and Tombstone Piledriving Linda McMahon on the steel floor and burying his brother The Undertaker alive. In that time, Kane feuded with Shane McMahon. After being thrown into a burning dumpster and sent in a limo crashing into a semi truck in previous weeks, Kane survived and defeated Shane in an Ambulance Match at Survivor Series. Kane continued to wreak havoc until WrestleMania XX when The Undertaker returned from the grave and defeated Kane in a match.
Chris Benoit and Eddie Guererro finally rose to the top. Benoit won the Royal Rumble in 2004 as the first entry. He stayed in over an hour, outlasting all of the other 29 competitors. He jumped to RAW via some strange loophole in the system and defeated Triple H for the World Title at WrestleMania. Eddie Guererro earned himself a title shot and defeated Brock Lesnar at No Way Out 2004 with some help from Bill Goldberg. Goldberg had a front row ticket to the Smackdown PPV. With a little bad blood already existing between the two, Lesnar called Goldberg into the ring during the title match. Goldberg entered, and eventually Speared and Jackhammered Lesnar. Eddie eventually hit his Frog Splash off the top rope for the win.
The APA was officially ended when Farooq was fired by Paul Heyman in March of 2004. Bradshaw saw this as his opportunity to make an impact as a singles wrestler. He cut his hair, returned to his natural blonde hair color, and presented himself in a full suit and a white cowboy hat. He has taken on ther persona of a financial analyst who has ruled the stock market. He is a rich, successful, self-made man who thrives on success, no matter what the cost. He preaches American values, especially those of Layfield America. He is rather condescending and the fans do not like him. He won the WWE Title from Eddie Guererro at the Great American Bash in June.
The Undertaker returned with a persona combining the American Badass and his classic Phenom characteristics. He will face John "Bradshaw" Layfield at SummerSlam for the WWE Title.
Jonathan Coachman turned heel at SummerSlam 2003. The wrestling world was sent into a panic. PFFFFFFFFT!
These are all the main points I can think of off the top of my head. They were the biggest stories, with the obvious exception of the last one.
TITLES
I'll post a link here too. I searched Google and found a history of all the title belts. It's up to date. That might prove a bit helpful to you.
Title Histories