This term needs to be defined somewhere! There is a lot of friction in the community because of disagreement about what Vanilla means.
In almost all other software, Vanilla is the 'Out of the box', plainest and purist version of a game or application. Therefore a minecraft server or client that is described as vanilla, should be unmodded, and without plugins or added custom software. A Minecraft Realm would be a good example of vanilla minecraft, whereas a bukkit server would not.
Yet, most servers that claim to be vanilla (as opposed to semi-vanilla) has either some form of area protection or teleportation commands that spoil the game for players who are interested in pure vanilla gameplay.