The word "look" is very general. It can mean to look for a long time, a short time, carefully, absent-mindedly, or in many other ways. "Take a look" is more specific. It means to look at something for a short period, usually for a specific purpose.
You can ask someone to take a look at something that needs to be fixed, or for something that's important for them to see. Here's another example from a science classroom. The teacher tells the class to look at something in the textbook: