The phrase "local coop" refers to a video game feature that allows two or more players to play together on the same console or device, usually in the same room. Full definition
If you are playing on local coop with friends, you can piggyback your friend then cooperate to pull a team attack. (gamecmd.com)
This is the point where players take over of the mischievous brothers, either alone in single player as Cuphead or in local coop with the second player taking over as Mugman. (xboxgamerreviews.com)
I'm not getting rid of my Wii U anytime soon, I love it for local coop games and I'd prefer the game still releasing on Wii U. (kickstarter.com)