Remember when your baby first discovered his or her hands and stared on them for minutes on end. This was by far one of the most entertaining newborn milestones.
When my son was about 2 months old, his vision was good enough and his dexterity developed enough to bring his hands into his field of vision. Once he could see his hands, he would stare at them. He'd open them out flat and then close them in to a tiny fist over and over again.
You could almost see his brain working. Indeed these appendages were new to him - as were all his little fingers. No longer were his arms just flailing about without direction. He knew that they were there, and that his arms were by far the most interesting things about him. During this time in his little life, it was like his hands were his favorite playthings.
I could almost hear him saying, "Woah, mom. Have you seen these things? They are called hands and they are amazing! Watch, look what they can do! Did you just see that? Woah. Totally cool."
This phase didn't last long but while it did, it certainly was entertaining - for both of us.