If someone is your friend, you'll see alerts in the game and on the website about what they've been playing and if they've dethroned you.You'll show up on each others' "friends" scoreboards, and you'll be able to see detailed information about each other's most-played songs and artists.
If someone is your follower, they'll receive limited information on the website about what you've been doing (most-used characters and thrones only). They won't show up on your "friends" scoreboards, and you won't show up on theirs. You can upgrade them to friend status if you would like them to show up on your scoreboards and see detailed information about your favorite songs and artists.
If you are someone's follower, this is like sending them a friend request. You'll show up on their list of followers, and they can upgrade you to friend status (showing up on each other's scoreboards, full access to their webpage info) if they choose to.