Check out this sweet little gif demonstrating Battlefield 4’s new leaning and cover system in action.
DICE actually has their own term for this, called zoom peek. As demonstrated above, while you stay behind cover, you can zoom your weapon in and you will automatically peek over the cover, allowing you to take shots at enemies. DICE’s Karl-Magnus Troedsson has explained that zoom peek is still a work in progress, but they decided to reveal the feature in events so that fans could try it out for themselves in multiplayer.
Zoom peek definitely looks like a great new addition and another visual flourish you can credit to DICE, aside from counter knifing, Field Upgrades, and many other stellar additions. It's fairly obvious this will significantly change gameplay for Battlefield, and first-person shooters, if implemented as is. Presumably DICE is still figuring out how this feature balanced out the entire FPS experience, but I'm sure many are looking forward to seeing this in the final game.