The order in which champions are picked is important. As an example, if you start by picking Katarina, the enemy might pick Blitzcrank, Soraka or any number of champions which can immediately shut her ult down. However, if you're last pick and the enemy doesn't have much hard CC, Katarina would be a safe pick!
In draft games players can swap champions after everyone has chosen one, so if your AP mid feels like Katarina might be a good choice but happens to be one of the first picks, s/he can choose a champion for a different role and defer the Katarina pick until it's too late for the enemy to react. But if the last pick on your team doesn't have Katarina s/he can't pick her and you won't be able to swap...
Well, tournament games aren't supposed to be about how many AP champions your support player owns! Your last pick player chooses a different (usually unpopular) champion and announces through chat which champion it really is. After picks are done in this fashion, the game is remade with everyone picking the champions they would have swapped to. In this case no one cares about bans as long as you don't ban anyone that was picked :)
You can also do this the other way around, having someone pick up a contested pick early on even if s/he doesn't own that champion.