Well, do you know what angular momentum is? An object's angular momentum has two parts. One part is due to the motion of the center of mass around the origin (orbital angular momentum). And another part is intrinsic to the object. For a compound object, you can break down the intrinsic angular momentum into the angular momentum of the constituent parts around the center of mass of the object. For a rotating solid object, the constituent parts are moving around the center of mass, so each part has orbital angular momentum which contributes to the intrinsic angular momentum of the object. But each part can also have some intrinsic angular momentum, and so on. We eventually reach particles which have no constituent parts. These have intrinsic angular momentum which we call "spin".