What, exactly, is Bukkit for Minecraft?

I've read the documentation and everything I can find on this subject, but I'd like to know:

• What Bukkit does that vanilla Minecraft Server does not
• Why people decide to use it over vanilla Minecraft Server
• What plugins do/are for

Background: I've only used vanilla Minecraft Server before, on my own machine. I can't quite grasp what Server Mods or Wrappers actually do, so this may be the source of my confusion.

Bukkit is a developer API - it basically provides hooks and functions that developers can use to plugin to Minecraft.

Craftbukkit is the server component you download that lets these plugins work with the official Minecraft server.

Craftbukkit is not yet a package manager, rather a server wrapper - plugin installation and managed updates are planned through another tool (fill.bukkit.org) but it has not yet been released - Bukkit itself is still under heavy development.

So, to answer your three bullet points:

What Bukkit does that vanilla Minecraft Server does not

Bukkit on its own does very little – it simply exposes an API that can be used by developers to add functionality to the game.

Why people decide to use it over vanilla Minecraft Server

People generally use it because of the additional functionality that can be added through plugins: area protection, a form of economy, the ability to warp throughout the world, and making minecarts more stable. A quick browse through the Bukkit plugin releases forum will show you some more possibilities.

What plugins do/are for

I think this is answered through the other two – they add additional functionality to the game. :)

Essentially, it's a package/plugin manager for Minecraft servers. Rather than installing addons separately, it allows you to do it through a central interface.

Bukkit's 'About' page actually does a great job of listing its selling points in relation to alternatives:

• lower server footprint
• increased performance when adding mods
• easy mod installation
• easier for developers to extend and customize the game via mods