These are friends on Facebook that you and another person have in common. That is, both of you know those people.
Robbie and I have 180 mutual friends on Facebook. How do I still not know who he is?!
"mutual friend" is a pseudonym for the internet, or an internet dating site, when used to cover "how do you know...?" "oh, we met through a mutual friend"
"how do you know so and so?" "Oh, we met through a mutual friend" (translation: we met through an internet dating site looking for freaky people who like this and that...)