Drawing conclusions means in general terms to come to the end of a written assignment. To draw a conclusion, however, demands that one has reached the end of a reasoned argument, ordinarily in response to a pre-determined question from an examiner of some kind.
The conclusion must make explicit reference to the terms of the original question asked but, in most cases, should not come be an absolute conclusion falling on one side of a debate, albeit that it may come down strongly on one side of an argument. However, in order to be a balanced conclusion, it must also be aware of alternative points of view and, even where it disagrees with them, at least address why that is the case and explain that such views are still legitimate.
Equally, a conclusion must come on the basis of the examination of evidence which should be the basis for most of the essay. In a literature essay, for example, the argument will form a number of assertions of opinion about the work of literature which will need to be substantiated by direct reference to the work in question and discussions of how these examples prove the opinions held. In the conclusion, a brief summary of these points will be needed to demonstrate why you have come to the final answer to the question that you have. Moreover, in more sophisticated literature essays, such a conclusion will also be made on the basis of examining whether one's own opinion fits in with or disagrees with the opinions of earlier critics. In a conclusion, a brief statement of how your own opinion marries with the opinions of earlier critics would also be a useful thing to do.
You can think of "drawing a conclusion" as coming up with a final statement that wraps everything up. It's like the logical statement of what comes next. For a really basic example, say you walked into school on Monday and your best friend was limping, even though he or she wasn't on Friday. You would probably naturally come to the conclusion that he or she somehow got hurt over the weekend and ask about that. Drawing conclusions is similar but often not as intuitive in a literary setting. Instead of actions that you can see and deal with in everyday life, you have to pick up clues from writing to analyze the literature. You can draw conclusions about how an author feels about a subject through the positive/negative connotations of the words used. For example, if the author describes a dog as being "fluffy and adorable", you can draw the conclusion that the author thinks positively about the dog. As the works you deal with becomes more advanced, the clues will become more subtle and you'll have to really look for them and interpret them as your experiences have taught you.
Drawing conclusions is, in short, taking the information you have read or know about the topic to predict a plausible ending for the situation. Sometimes, it may be necessary to look at the traits of the characters and their actions throughout a story. It is also important to consider the events that are leading to this point.