A 3 team trade in basketball is when three different teams work together towards a deal to trade players, draft picks, or cash between themselves, where a team's assets can go to either of the other two teams involved in the trade, while also receiving assets from any of the other two teams. This type of deal is very common in the NBA; 3 team trades gives teams more flexibility when shipping out or looking for players to acquire, while it is also harder to close, since all three stakeholders should be happy with the trade, while in a regular two team trade, only two parties must agree.
Imagine a scenario where team A really wants to acquire a center from team B. However, none of team A's draft picks or players interests team B, and so they can't reach an agreement. Now, team C is interested in team A's point guard, and they have a very good draft pick, which definitely gets team B's attention. That way, all three teams can agree in a trade where Team A is getting the desired center from Team B while sending their point guard to team C; Team B gets the valued draft pick from Team C while sending their center to team A; and Team C sends their high draft pick to Team B while receiving the point guard from Team A.
In that case, teams worked together to reach a deal that wouldn't be possible if not for a three team deal. That is just one example of many of how a 3 team trade can help teams. Some other trades may also be impossible to complete because of salary cap limitations, and a 3 team trade can make it work.It is also common for two teams to be negotiating, and a third team asks to join the trade. That can be beneficial for all parties as there are more assets to choose from and many more trade possibilities.
A recent example of a three team trade in the NBA is a deal involving the Cleveland Cavaliers, the Milwaukee Bucks, and the Washington Wizards. Cleveland was rebuilding and looking to trade veterans for young players or draft picks, while the Bucks were looking to get experienced players to help in their soon to come playoff run. Washington was looking to make their salary sheet smaller. Take a look at that trade below: