I've played a decent amount of Shadowrun 3rd edition, and recently joined a group of players who play 4th ed. I know I'm going to get confused and turned about- In summary, what's changed that I should reread about, and what's similar enough (but different in an important way) that I would otherwise assume is the same and would get tripped up about?
Shadowrun 4 uses a largely different mechanic from Shadowrun 3: SR4 uses the new World of Darkness dice mechanic rather than the classic Shadowrun mechanic (except they use d6 instead of d10, but 66.7% and 70% are basically the same probability...). The justification for the change was to speed up combat and other conflict resolution, which it does to some extent, by not having to keep track of both target number and number of successes (all target numbers are now 5; some things have thresholds for the number of successes you need--all the math is just done on # of successes). Also, dice pools are gone, so there are many fewer tactical decisions to make, also speeding up the process. (If you enjoyed selecting just how many combat pool you were going to use for soaking so you had enough left to take out your next opponent with one shot, you will be disappointed. If you were annoyed that you had all these extra decisions to make when you really just wanted to kill the bad guy as quickly and effectively as possible, you will be pleased.)
Because of the drastic change to mechanics, SR4 is a dramatically less versatile system; it works with a much narrower range of abilities and difficulties. On the other hand, the game has been balanced so that a normal run will be right in the middle of the sweet spot where the outcomes in SR4 do not feel drastically different from SR3. So if you were doing standard runs before, and will be again, you can take advantage of the simpler mechanics without much loss. SR4 breaks badly as characters or NPCs become extremely powerful (e.g. you need an impossible number of successes to defeat them, with d20-style "I stand in the middle of a room full of goblins for hours and they can't hit me" scenarios), so there are various caps and limits that were much softer before; starting out, you can make a runner who comes pretty close to the best in the world in something. Whether you like that or not is personal taste, but it is definitely a difference.
Anyway, the take-home message is that you should be prepared to feel like you're playing with different mechanics. The same concepts are mostly there in some guise, but it scarcely would have been more different if they had switched to d20.
Despite the mechanics changes, the setting feels much the same as before. Otaku are now Technomancers, and the old separate-worlds idea of the matrix has been replaced by a parallel augmented reality version that greatly helps with integrating deckers (now hackers--no more decks!) into the flow of gameplay. The timeline has advanced another decade or so, but aside from the crash of the old Matrix and replacement with the new augmented reality stuff, there's nothing that will radically change how your character approaches the world. The new mechanics are balanced to yield similar outcomes for standard runs, so you'll be approximately equally worried about a team of security guards or whatnot; if you were using SR3 the way you were "supposed" to be, you'll mostly just notice that SR4 runs a bit faster and that you can see your decker face-to-face.
A major change setting and mechanics-wise has been made to the Matrix.
In 2064, the Matrix was brought down worldwide by the epic battle between a rogue megalomaniac AI and those who would prevent it from attaining virtual godhood, flatlining a number of the deckers connected at the time (cf. System Failure). This led to a move to wireless technology, with the Matrix now being an Augmented Reality layer accessible from everywhere Wi-fi is available. Connection to the Matrix is commonplace enough that not being visible on the grid can raise suspicions.
As a consequence of the change in technology, interaction with the Matrix is now on the same time scale as the rest of the game (though VR and hot-sim grant additional Initiative passes), so the other players are not put aside while you're hacking.
Otakus have been "replaced" by Technomancers. Their numbers exploded since the Second Crash, many of them being survivors of the event. Contrasting with their predecessors, Technomancers don't need any 'ware installed and are not subject to the Fading that progressively diminished their connection to the Matrix. While they are still a mysterious phenomenon, the world at large is acknowledging them and trying to understand the Resonance.
Just copying my answer from this very similar question:
We have been playing a Shadowrun 4th Edition game for a very long time now. I find the rules system to be much easier to understand/operate, and the dice rolling is pretty straightforward. I have been playing Shadowrun since 2nd Edition, and personally, I think 4th is the best yet.
Setting wise, the biggest new addition (as Numenetics stated) is the wireless Matrix. Also, now that machines are talking with WiFi, so are Meta-Humans - The Technomancer, a "hacker" that uses a Magic like stat called Resonance to "Thread" bonuses to programs, and summon "Sprites" to do their bidding is now a character option.
There are a lot of great optional rules, like taking "automatic successes" (your dice pool / 4 = number of hits) which allows you to quite easily run a diceless forum game alongside your sit down game. We have taken full advantage of that system in our very long campaign...
The main system difference is that the "Target number" for rolling is ALWAYS 5... I.E, 5 and 6 are the only #'s that ever "hit". 6's do not "explode" like in previous versions unless you use your "Edge" stat. Also, instead of increasing or decreasing target numbers, things increase and decrease Threshold/Pool size.
I would be happy to try to address more specific inquiries into the 4th edition as well, if there is something you were interested in knowing that I didn't mention...
From a friend who plays extensively, I understand the setting is quite different - in his words, the one mistake they made was making everything wirless-enabled, including cyberware. A good hacker can essentially neuter a street sam.
Copying some details from a forum post I found about mechanics...
Difference from 3rd to 4th: Complete system change, None of the books are compatible with older systems. Instead of having different target numbers you have a static target number with differing dice pools. The magic, decking, rigging and other systems have pretty much been copy pasted with just a few name changes put in (or thats how i read it anyways), it makes it easier for new players though. Also character gen has gone from a priority system as basic to being a point buy system as basic.
History wise the time line pretty much gets advanced with each edition.
1st and 2nd was late 2040's - mid 2050's (i think) 3rd was mid 2050's - mid 2060's 4th is 2070+