Martial arts are a great full-body workout. Strength training with free weights or weight machines is very effective for building specific muscle groups, but often results in certain muscles being ignored. That's why many people refer to the difference between "gym strength" and "functional strength". Overemphasizing some muscles in the gym while under emphasizing others leads to a lack of true functional strength, and can also result in injury due to undeveloped stabilizer muscles.
Since martial arts -- particularly Brazilian Jiu-Jitsu -- require use of the entire body, developing full-body strength is a side effect of training.
Weight Loss and Cardiovascular Health
Performing training drills and sparring are both high intensity workouts which improve cardiovascular health and promote healthy weight loss when done regularly. As an added benefit, they are both extremely fun, so you'll rarely be thinking about being tired while exercising.
Self Esteem, Self Confidence, and Mental Toughness
One of the best ways to build self esteem and mental toughness is to get good at something that is difficult. Getting good at a martial art requires dedication and a lot of practice. The longer you train, the more your self esteem will improve because you'll know that you've accomplished a goal that you set for yourself, and you've developed a skill that not many people have. You'll also get the mood benefits that come from regular exercise.
Additionally, you'll develop the self confidence that comes from knowing that you're capable of defending yourself if need be.
Exercise has been scientifically proven to be one of the best ways to relieve stress and improve mood. Even if you had a stressful day, you'll be amazed at how good you'll feel by the end of class.
Being a Part of a Community
Martial arts classes are great for developing a sense of community. New students are helped by the instructors and by senior students. Then as those junior students become more experienced, they begin to help new students themselves, and so on. This cycle is great for building a community of friends who all share in each others successes and accomplishments.
The nature of martial arts schools cultivate groups of humble and kind individuals. Since newer students will generally lose sparring matches to experienced (and often smaller) students, people who are bullies or are too egotistical often quit. The result is that the students who remain in martial arts classes focus on training and improving themselves, not "winning".