From Diablo Wiki
Blizzard has implemented a Friends List into Diablo III, for easier connection to buddies.
The Friends List is integrated into the new BattleTag system. In this way friends are added not by character name or account name, but by the Battle Tag each player must create when they first log onto Battle.net via Diablo III. Thus a friend name is their Battletag, and being someone's friend allows them to always see when you are online, no matter which of your Diablo III characters you are using.
Cross Game Chat
Since your Battle Tag applies to your entire Battle.net account, every game tied to your account functions through it. Thus the Friends List allows cross-game chat and friends, and people n your friends list can see you online and send you messages even if you're playing Starcraft 2 or World of Warcraft.
Friends List Function
Adding Friends is very simple with the the BattleTag, as the BattleTag FAQ explains.