To look at - When you look at something (or someone) you are interested in the appearance of that thing or person.
Generally we look at things that are static.
Look at these photos, they're really good.
To 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.
!Note - 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!" you can take it as a warning.
See also see vs watch.