There is absolutely a campaign aspect and PVE to the title. You can play with up to four people in a squad that is drop-in drop-out. There will also be matchmaking if you dont have any friends who pick up the title on day 1.
Division is more like Borderlands than it is anything else. There is skill trees with upgradeable skills as well as five different qualities of loot ranging from common to legendary. "Loot" is very rare in that you wont receive a loot drop for everything you kill. So there is an element of collectibility if you will in that you might have to horde something early for later in the game, which you can store at your Base of Operations.
Base of Operations are unlocked by completing tasks within the campaign of the game. When you extract a piece of gear, this is where you will go to pick it up. There are multiple Bases of Operation through out the city each with their own plot line and plot ties.
If they didnt take it out, for whatever reason, if you have two Base of Operations or more, supply lines between each Base of Operations will be created. Again, this was from 2-3 years ago when the game was first revealed. The game has been in development for close to five years so things can change due to balance issues, such as the melee mechanic.
So to answer your question a little bit better, there is a ton of content to do with your friends between loot hording, gearing up, changing skills to fit the needs of your party (Division is a classless game which means you can respec your skills at any time, which helps if youre playing by yourself.), opening Base of Operations, PVP and PVE.
Alot of the "Story" portion has not been revealed to the public yet and I cannot speak on behalf of that as I am under NDA.