From Diablo Wiki
Profiles are Blizzard's term for all of the characters on an account. A profile fully encompasses the state of your account, including all your kill tallies, items, equipment, characters, achievements, etc.
Players can view their own and other players' profiles in-game, or via Blizzard's website, or via numerous third party websites that display character information, items, and more. This sort of viewing has some privacy, as the profile shows only character equipment, follower equipment, and skills/passives. It does not show a character's gold or blood shard tallies, stash contents, inventory contents, or Paragon Point distribution.
To view a profile in-game, right click on a character's name, then select the option from the drop down menu.
Profile Feature Introduced
Blizzard first enabled profiles in August 2012, a few months after Diablo 3's launch. 
Profiles give you the power to:
- View your heroes’ gear, stats, and skills. How high have you raised your characters’ attributes? What are they wielding in each slot? What are their most prominent gear bonuses? What skills comprise their current build? Nuance awaits you in the Heroes tab.
- Track your game progress. How many acts have you cleared? What bosses have you shredded in each difficulty? How far have you leveled up your hardcore and normal artisans? Find out in the Career tab. You can also check your play time (by class) throughout your entire Diablo III career, and learn how many monsters and elites you’ve slain.
- Share with your friends. The Friends tab lets you check out your BattleTag friends’ characters, so that you can quickly compare notes on gear, skill & rune choices, and everything in between. You can also click on a BattleTag in the Diablo III forums to go directly to that player’s profile.