A new version of Battlefield naturally means a new version of its surrounding support structures, like the 'Battlelog' social layer that launched with BF3. DICE has outlined the changes coming to Battlefield 4's iteration in a lengthy Battlefield Blog post, including giving more detail on the asynchronous 'Missions' you can set for your friends.
Missions are challenges which let you compete with friends even when you're not all on at once. You can create a mission by setting objectives outside the usual perimeters, and have up to four friends compete to earn them. Once you've set an objective and a map, you can set the amount of attempts your friends will get. From there, they'll have 48 hours to complete it. The Battlelog will alert you when you're invited to an event, including on the new mobile app, to make sure you don't miss an invite. The mobile app can also be used to create missions on the fly.
DICE doesn't mention any particular awards to competing in missions aside from bragging rights, but it says it will be adding new selectable objectives as time goes on.