I'm new to development which is why I ended up here because of wanting to know what exactly Forgebukkit is - and my understanding from reading all of this, please correct me if I am wrong, is that forge is what better supports the Minecraft modification itself, like blocks, recipies, mobs and etc, making it easier to have it work on a multi-player server for all the players to interact with. As for the bukkit part of the name, it's what includes the bukkit API allowing the server administrator to run the bukkit plugins which is needed more or less.
That being said, forgebukkit is what makes the mod playable on a multi-player server between players, which also allows more functionality from bukkit plugins.
@keepcalm Would I be correct in saying this?