Let me break it down for you:
Nearly all online gaming services (Xbox Live, PlayStation Network, Steam) require you to have a name (Mad Bad Coyote, nightunderafullmoon, HamillianActor,). I like refer to these as Gamertags, because thats what they're called on Xbox Live. (PSN = PSN ID, Steam = Usernames, etc.) However you can call them whatever you want.
Steam is basically Xbox Live for computers. It allows people to connect with your friends by adding them to your Friends List.
Steam also allows you to create groups. These groups allow people within them to see if others within the group are online and communicate with them through chat.