The benefits of solving puzzles and quizzes are twofold. First, the brain is an organ which performs better with regular workouts, just as other bodily organs do. Think of these workouts as Mental Aerobics! Regular exercises and challenges to the brain will keep your mind healthy and active, ensure that there are active neural connections, improve mental associations and retrieval paths, and may stave off dementia in later years.
The second benefit is that our workouts are designed to exercise different parts of the brain. They encourage you to think laterally, so you learn to look at problems from several different aspects rather than the obvious approach. This is the kind of mental training that can help you to improve your problem-solving approaches in day-to-day life, and possibly to improve your test scores.
NOTE: These workouts are provided for the above reasons and are not IQ tests for Mensa.