This phrase comes from textbooks, where it is meant literally. The author presents some information, then presents a problem or question involving the information just taught, works through a partial solution, generally of the most difficult part, and then rather than take up a lot of space with details of calculations or a rehash of material discussed in previous chapters, says that the remainder of the problem is "left as an exercise for the reader". That is, the reader should be able to work out the remainder of the problem himself, and probably should do so to be sure he understands the material.
The phrase is sometimes used as a joke. When a writer gets to the difficult part of a problem and he doesn't want to take the trouble to solve it, or doesn't know how to solve, he says this is "left as an exercise for the reader", as if it was too trivial to waste space in the book discussing, when really the issue is that he can't figure out the answer himself. Like, "When you go hiking, bring a bottle of some tranquilizer, like Valium, with you. Then if you are encounter a grizzly bear or other dangerous wild animal in the forest, simply give him two of these tranquilizers to calm him down and you can safely pass. How to get the bear to take the tranquilizers is left as an exercise for the reader." Like any joke, whoever first used it was a clever comedian, but it gets tedious when overused.
The literal usage is inappropriate in a technical book that is not presented as a textbook with exercises. As a joke, whether it is appropriate depends on the overall tone of the book.