The Home Limit, as determined by a player's Mane Character, is the amount of Friends that a player can have at their home at the end of their turn. (The Mane Character card does not count against the Home Limit; for example, if a player's Mane Character had a Home Limit of 3 then that player could have three Friends and the Mane Character at their home area and that wouldn't count as exceeding the Home Limit.)
At the end of a player's turn, in a situation where there are more Friends at that player's home than their Home Limit allows, such as during a faceoff resolution, that player must retire (place into their discard) a number of their Friends until the limit is not exceeded.
Note that your home limit is only checked at the end of your own turn. There is no limit during your opponent's turn (so if they start a problem faceoff which sends lots of friends to both homes, only they need to resolve their home limit; you still have until the end of your next turn before you need to resolve your own home limit).