Especially, the "what's-her-name" part.
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Much used if someone doesn't know the name of the person being talked about.
"I met what's-her-name yesterday".
Usually being used if the person listening also knows the person.
In general that term is used in place of the actual name when the speaker doesn't know the name. Note that it's pretty flippant in tone; if you don't want that tone you would just say "her."
In that context specifically it's being used as a joke, because of the twist of making someone feel special when they can't even remember her name.
I think masarah and jhocking pretty much covered it - I would simply add that the joke becomes rather more subtle if one considers that one (usually) knows one's mother's name - but (almost always) never uses it.