What is the difference between a CraftBukkit (Bukkit) server and a "vanilla" Minecraft server?
A "vanilla" Minecraft server essentially means that it is unmodified and is in the original format direct from the creator (Mojang). You can download this version directly from the Minecraft website. It has no support for plugins at all, but there are server mods that will work which will require you to modify the internal contents of the server file itself.
CraftBukkit, on the other hand, is a modified version of the vanilla Minecraft server file. The Bukkit team has modified in such a way that it allows for plugins to be used with the game, even though it did not allow for such features originally. This is both a good and bad thing. It is good in that you are able to use plugins to expand what is possible with a vanilla server and to make gameplay more enjoyable. However, since CraftBukkit and all plugins are created by third parties and are unofficially supported, there are bound to be bugs which can cause anything from lag to server crashes. Despite the issues, the fun factor usually outweighs the problems, thus all of our servers have CraftBukkit installed by default (you can use vanilla too if you want).
The separation of vanilla Minecraft, CraftBukkit, and plugins is what causes a lot of problems whenever Minecraft is updated. Since CraftBukkit and plugin developers do not work directly with Mojang (the developers of Minecraft), they have to wait for the update to come out first, just like all regular users. Thus, whenever Minecraft is updated, CraftBukkit may have a delay of several hours to a few days before they can even release an experimental (read: unstable) build. It takes a bit longer for a recommended (read: stable) build to be released. Once CraftBukkit has reached a stable build, that is when plugin developers will actually start to update their plugins to support the latest CraftBukkit properly since experimental builds of CraftBukkit change too often for them to keep up.