"Look" - simply means just that. To gaze, to perceive something with your eyes. It is a very general term. Example: "When I entered the room, I found him looking at me with wide eyes." "Have a look" - implies that you are observing something and there is a particular reason why you are doing it. Perhaps you are investigated something and want to "have a look" in order to figure something out. Example: "Let me have a look, so I can see if there is anything else that needs to be done." I hope this explanation helps.

Just to add to Lee's answer, these are often used as an introductory word or phrase with little or no grammatical relationship to the rest of the sentence: - Look, I know it's expensive but we need to buy it anyway. - Have a look at this, does it seem too tight? The first version is very often heard on TV talk shows.

if you say "Have a look" instead of just "look" it's like you are trying to solve a problem, or that what you are looking at is unusual. like, "The engine doesn't work. The mechanic will have a look at it." or "That's a strange picture. You should have a look at it. " "take a look" is the same as "have a look". In America, "take a look" is more common.