When you look at someone or something you are interested in the appearance.
Generally we look at things that are static.
Look at these photos, they're really good.
I went to the art gallery to look at the exhibition of paintings.
Watch is a verb.
When you watch someone or something you are interested in what happens.
Generally we watch things that move or change state.
I watch TV every night.
The security guard watched the shoplifter steal the clock.
If I say to you "Look at him!" I mean for you to check out his appearance. But, if I say to you "Watch him!" I mean it as a warning.