Nine or 24 of your closest friends
We might as well start the explanation with head count. While you can play WoW and feel relatively fulfuilled by doing everything all by your lonesome, the average WoW player is really a social critter.
As we level up, most of us group with four other players and go do dungeons together. The dynamic is much different than playing by yourself. Three people focus on killing the boss, while one person heals and one person absorbs all the damage. (That's the DPS, healer and tank roles, by the way.)
Once you're at maximum level, you have the natural inclination to fight bigger, badder bosses. The way Blizzard conveys a sense of epic proportion to these final non-player characters is to require more than a mere five players to kill them; you need 10 or 25.
Since these bosses are fundamentally different from the casual 5-man groups to which you're accustomed, we refer to them as a raid bosses. You can fight raid bosses in a 10-man group or a 25-man group, depending on the size of the raid you're attempting.
How raid bosses are different
Raid bosses are more difficult to kill than any other creature in the game, even above and beyond the fact that you need more people to kill them. These bosses have a whole string of special attacks and freaky requirements. For that matter, just having 10 or 25 people to kill them isn't enough; usually, those raid members must all be in superior gear than that of your average dungeon runner.
The additional complexity and resulting coordination required lead to raid groups must be highly organized (well, highly organized compared to your average random dungeon group). You tend to have a raid leader, at the very least; this is the person responsible for getting all of the members together. Raid leaders tend to be responsible for explaining strategy, calling the shots, and getting everyone to perform as well as possible.
Of course, if you're going to all this trouble to kill an epic big, bad boss, then the reward had better be above average. Therefore, you get two raid rewards for completing contemporary raids.
First, the bosses drop raid loot. While epic items are all throughout the game, only the contemporary raid bosses will drop the best items. If you want to kit out your character in the best gear, you'll have to kill those bosses.
Second, you'll get valor points. While you gain limited amounts of valor points from completing random dungeons, the lion's share of your weekly valor points come from raiding. You get to spend the points, therefore, on some pretty darn sweet gear.
As an added bonus, some tiers of raiding include a reputation gain. When you kill mobs and bosses inside a raid instance, your reputation with an associated faction will slowly grow. This is a good way to make sure that raiders see some gear improvements, even if they're struggling to kill bosses.
Of course, there are a few permutations involved in standard raiding. There are three modes of raiding in the upcoming patch: random raiding, normal raiding, and heroic raiding. The normal difficulty is your baseline level of the raid. If you join the raid through a random group, the difficulty is turned down slightly to account for its being a previously uncoordinated group.
Heroic modes are especially difficult; the bosses do more damage, gain new attacks, and generally require an even higher level of player skill to overcome. For this reason, heroic modes drop even better gear than counterpart raids.
Is it worth it?
Of course, you have to ask yourself if raiding is worth it. People spend half a dozen to dozens of hours every week raiding. This is a question that can only be answered on a personal level. Some people enjoy the difficulty and challenge of raiding; other folks find it a time sink.
The best way to figure out if you think raiding is worth it is to jump in and give it a try yourself.
Visit the WoW Rookie Guide for links to everything you need to get started as a new player, from how to control your character and camera angles when you're just starting out, to learning how to tank, getting up to speed for heroics and even how to win Tol Barad.