It’s a feature added in FIFA 21 that lets you team up with a friend online in Division Rivals against other solos or duos, in Squad Battles against the AI, or kick back in FUT Friendlies House Rules and Public Co-Op against other players.
In FIFA 22, there is a new friends widget, which is accessible through most of FIFA Ultimate Team by simply hitting R2 or RT. From this widget you can select a friend to play a game with and be taken straight to the Co-Op lobby.

Invite Friends
The person who sets up the lobby will become the Captain, meaning that they have control over which of their squads will be used for the match and what game mode you will play. From the lobby, both players will see the Captain’s top-rated players from their current active squad and when both players are ready the captain will have the ability to start the game in the chosen mode.

FUT CO-Op is available for both generations but you won’t be able to play across console generations or cross-play in FIFA 22. You and your friend will have to play online on the same console (for example, you cannot be on a PS4 and he/she is on a PS5).
On the pre-match screen, you can see the connection bars of both connections (you and your friend).
Using the FIFA Trainer in a Co-Op game will show the inputs for both players on the team as they’re happening. This will allow players to see what their partner is about to do, enabling them to react to the on-screen displays. This helps in setting up the right runs without a need to rely on voice communication exclusively.
FUT 22 does not have support for game invites from Co-Op sessions, not even on FUT Friendlies. In other words, you cannot play against other friends picked by you. You will always face random opponents.
Yes. There is a toggle that lets you choose between a mix of solo players and Co-Op groups in your matches, or just vs solo players.

Playing online cooperatively with a friend is only possible in Squad Battles, Division Rivals and FUT Friendlies. You cannot play FUT CO-Op on FUT Champions or FUT Draft.
In Friendlies, you can pair up to play together and, using in-game matchmaking, find people to play any of our base Friendlies experiences. The matches will follow the ruleset chosen and rewards will be the same as playing Friendlies solo. This is a great way to try out some new player combinations, teams, or to just work on your team play in a risk-free friendly environment.
Classic, Mystery Ball, Swaps, King of the hill, Max Chemistry, Headers & Volleys, Survival, Long Range, No Rules and Co-op Public Matchmaking (new addition in FIFA 22).
It’s a new Co-Op mode in FUT Friendlies. The goal of this mode is to have a casual drop-in experience playing FUT with a new partner against other Co-op opponents.

In Online Friendlies, you’ll see the new game mode. From here, you’ll enter into a new team select screen with a list of pre-made Squads. You won’t be using your FUT squad in Public Matchmaking, instead, we’ll have unique Squads that will be changing on a regular basis.

This avoids a situation where both co-op partners want to use their own Squad. It’s also a great chance to try out some of the best players in FUT. The Squads will reflect recently released Player Items in the game, so you’ll see appropriately balanced teams.

Invite Friends
For Division Rivals specifically, matchmaking will be done using the divisions of the duo. In Public Co-Op , you will play against players who picked the same preferred squad.

Selecting one of the Squads will start a search for a partner, and your choice acts as your preferred Squad to play with. If the game can’t find a partner looking to use the same preferred Squad, it will expand the search to look for partners using all of the possible Squads. When all possible Squads are being chosen, the squad choice will be assigned at random, so there’s a chance you may play with a different Squad if the search for a partner is expanded. Once you’ve found a partner, the system will then matchmake you with another co-op pair who are also using the pre-made Squads to play against. If a match can’t be found, the agme will expand the search to anyone playing Co-Op Friendlies before expanding further to look for an Online Friendly Classic Match where you’ll play 2v1.

Public Co-Op Squads
In Squad Battles and Rivals, based on the result of the game, each participant will earn their coins for the match using the regular in-game calculations. In Co-Op Friendlies, rewards are the same as playing Friendlies solo.
Playing together won’t only take place on the pitch in head to head gameplay. In FUT Events you can collaborate and compete by completing Objectives in-game to unlock rewards as a community. In FIFA 21, two new types of Events were included into Objectives:

Community Events
With Community Events, each player who completes Objectives in specified groups will contribute to a global XP pool. As this pool of XP grows, the community will progress towards thresholds that unlock rewards for everyone who’s completed at least one objective in the event.

Team Events
Team Events will divide the community into different teams to compete head to head for rewards. Joining a Team is easy, when you start the Event you’ll be given the choice to support one of up to five Teams each with its own set of Objectives and rewards. Competitions are balanced based on which Team’s members are contributing the highest XP on average for the event. So once you’ve chosen your Team, start completing the Objectives to help your chosen side in the leaderboards. At the end of the competition, the winning team will be rewarded with new customization items to show off your allegiance, Coins or Packs. The types of rewards available will change with each Event throughout the year.