When raiding there are a host of addons out there that can help - from addons that are specific to your class and/or role, to those that are more related to specific fights and bosses. In order to maintain your addons (ie, make sure they're kept up to date), there are also various addon managers that will check and install updates for you. Below are some examples of addons that we either consider necessary in order to raid, or useful.
Deadly Boss Mods
Deadly Boss Mods is simply a "timer" of sorts to various boss events - how long until the next cast of something, along with, often, a suggestion of what to do when that cast happens. This addon is so ingrained into WoW raiding now that Blizzard tune their fights assuming that people will use it.
Weak Auras, in itself, does nothing. It is a platform or base in order to add your own selected plug-ins. From a raiding perspective, these can include plug-ins that run alongside Deadly Boss Mods that give you more information about what to do, and when and, often, do it in a way that is hard to miss in the heat of a fight. There are also plug-ins for specific classes - like spell rotations or cooldown indicators - and loads of other useful stuff. Essentially if you're struggling to do something in WoW, there's usually a plug-in for it.
Ask Mr. Robot
This is a combination of addon and website - you can use the website without using the addon, but the addon makes things more streamlined. Essentially, this checks your character's gear and suggests what enchants, gems, etc, you need on your character. For a small subscription you can also use the addon to upload the gear you have in your bags, so that the site can suggest the best gear combination. This is a great site if you're just not sure if you forgot a gem or enchant somewhere, or you just want something to give you an overview of what stats you should be looking for.
A very useful addon, primarily for healers but actually can be used for any class. It "automates" the "mouseover" macro so that any mouse/key combination you set, can be used on raid frames, party frames, etc. You can also create macros - for example a druid could use the left click on a party member and, depending on whether or not they are dead, or in combat, it will either heal them, battle rez them, or simply rez them normally. A DK could use it to battle rez a raid member, without having to know where they are, or where that pesky, hardly ever used, button is .. just set a button/button combo for it and hover over the dead on the raid frames.