A friend is a mutual follow. That means you follow the other user and they follow you back. Mutual follows appear in the Friends section of your settings. If either person unfollows the other, the relationship is no longer considered a friendship and it will disappear from the Friends list.
When you follow someone, they are added to your following list and you are added to their followers list. If their account is public, the follow is approved right away. If their account is private, your follow stays pending until they approve it.
If your account is private, new followers must be approved before they can follow you. Pending requests appear in your Friends settings, where you can approve or decline them.
You can control who can open your followers list and following list from your Privacy settings. Depending on the setting, a list may be visible to everyone, only friends, or only you.
These settings affect whether people can open the full list from your profile. Your profile may still show follower and following counts even when the list itself is private.