Other forms: counterclaims; counterclaimed
When one person sues another in a court of law and the defendant responds by filing their own lawsuit against that person, that's a counterclaim.
If your neighbor sues you because you're collecting junky cars in your shared driveway, you might file a counterclaim stating that they stole property when they hauled one of the old cars to the town dump. Another way to use this word is to mean "opposing argument." In a debate, when you state that school lunch should be free for everyone, your opponent may present a counterclaim that the income from selling food helps the school in the long run.