A literature or "lit" review is a section of a paper that establishes the previous research done on whatever topic you're writing about. The point of a lit review is to show that you've done research in this field and to also establish a gap that your paper is aiming to fill. In talking about the previous research that's been done, you're also evaluating the sources' strengths and weaknesses.
The important part of a lit review is synthesis. You're not just making a list stating, "this person wrote this and then this person wrote this". The goal is to read a portion of the research done on your topic and evaluate it. A literature review is not a just a summary, you are actively comparing, contrasting, and (again) evaluating each of the works you are writing about creating an analysis of the current research on your topic and how you will contribute to the body of existing research. In other words a literature review is: "the story so far..".
They show that you understand what the current research is on this topic and that you're research will contribute to the body of work on this topic in some significant way. You can also write it as its own paper to describe or organize the body of work related to a topic or explore different aspects of an issue/problem.
There is more than one type of literature review. Check your professors assignment instructions first and then check out the resources below to see which type will fit your project best.