Faction servers are mainly desinged for players that are into compitions in factions you can make your own faction (clan) and build a base you can go to war with other factions or make allys with others. You can gain power by inviting other players, killing others in player vs. player battles or playing more on the server. For more information about factions message me.
To answer a faction invite just do /f join <faction name>
You use /f leave [faction name]
I assume you're talking about a faction invite. the command is /f join <faction>
If you are in a faction, and want to teleport to your faction home, just type /f home.
add them to your faction with /f join <faction name>
Press T
You will need to the faction plugin for bukkit once running then do in the chat /f create {name of faction here}
description
You kill mobs and players
someone who moderates the factions
You pretty much said it yourself. It's /f disband [faction tag]
Factions are kinda like groups or colonies in Minecraft. I'm in a faction on one server called PIEmasters (even though I hate pie >:D).