On Facebook mutual friends are those that two other users have in common. For instance, if you are friends with Jack and Ted, and Jack is friends with Ted, then Jack will show up as a mutual friend when you view Ted's profile.
You can discover the number of mutual friends you have in common with another user on that person's profile. Go to their timeline, and beneath their cover photo, you will see the number of mutual friends you have beside "Friends." Mutual friends may also be found through the "People You May Know" feature, which factors mutual friends into its friend-finding algorithm.