Fisticuffs is the act of fighting, or boxing, with bare hands. A heated argument can sometimes end in fisticuffs, with both participants punching wildly at each other.
If someone says to you, "Let's take this outside and settle it with some fisticuffs," it means you're likely to end up in a street scuffle. This seventeenth century word isn't too common these days, but it's a colorful way to say "fistfight." The word's form may imitate handiwork, or it might be based on the now-obsolete adjective fisty, "related to the fists," combined with the verb cuff, or "hit."