To provide context, you need to take the issues touched on in the presentation (problem, method, results) and see how other publications have addressed them. You are trying to provide an overview of the other work in the field that is related to the paper under consideration.
Remember that you only have 20 minutes. Please be careful to focus as best you can. If your literature search shows there are many alternative approaches to the same problem, try to enumerate them and compare them as best you can. If you don't find very many approaches to the same problem, talk about other places where the method has worked. Given the limited time, don't try to cover everything -- stay close to the paper for which you are providing context
After you have read the paper that you are providing context for, you have to do a literature search for related papers. A good place to start is the list of references in the paper. But don't stop there! Use the computational tools available to you. Look up the paper in PubMed, and click on the "related articles" link. Use the Science Citation Index or CiteSeer to help you find related articles.
In your background readings, look at alternative formulations for each of the issues in the paper. Try to identify where the main contribution of the paper is. For example, some papers define interesting new problems, but apply relatively straightforward methods to addressing them. For a paper like that, focus on work on related problems, and how the new problem statement differs from them. Some papers present a new approach to a well studied problem. For those papers, carefully compare the new method to other approaches people have taken to the problem. Also, in that situation, the choice of the evaluation method (used to compare the new approach to existing methods) is an important place to focus.
Context presenters should be looking for unstated assumptions made in the paper, and try to make them explicit. For example, does a paper on finding cis-regulatory elements from sequence and gene expression data assume that the elements are independent of each other? That the position of the element with respect to the start of transcription is unimportant? Reading alternative approaches to the same problem will make it easier for you to identify these assumptions.
When I first started teaching this course, the second presenter was called the "critic" and not the "context". The first presenter was supposed to say what was good about a paper, and the second what was not good about it. This turned out to be hard for many students, but I still welcome critical (either positive or negative) remarks, so long as they are well justified. Don't just say "this paper was really good." Say "The careful comparison of method x to method y in situation Z, demonstrated that it is important to ..." or "the evaluation section of this paper was unconvincing because the test set used was not particularly representative of the difficult aspects of the problem, which are...."