A second friend is a friend of your friend. They typically do not hang out with you unless you are hanging with your friend in common (known as a first friend). This is because hanging out with a second friend is usually awkward, as usually the only thing you have in common is that you both know your first friend. Sometimes if you spend enough time with a second friend, they can upgrade to a first friend. Then hanging out with that person is no longer awkward.
Say that Paul is your friend, and that David is his friend. But, sometimes you hang out with David because you hang out with Paul.
Michael: Hey man, you going to David's tonight?
Me: Is Paul going to be there?
Michael: Nah man, he's out of town.
Me: I probably won't go, he's more of a second friend.