You can animate in gimp or really in any number of programs. In short, the animation itself is comprised of different layers, each layer is different and determines how the object or character or subject behaves. For a more in depth explanation, I'd check out a few tutorials.
Really smooth animations and great pixeling. My only issue is as with so many games that use idle animations. There's almost too much movement for a character standing still. Those bottom two are perfect examples, if he kept throwing his body forward and back so much, he'd be tired very quicky, same with her and the constant throwing around of the swords. I think a little more subtlety on the movement and these would be perfect.