Everything said about karate for kids of course also applies equally to adults. However, for adults, there are a number of additional benefits to be had and skills to be learnt. Meditation and special breathing methods are also thought for adults.
Karate is whole body training, and it works on both the body and the mind. It develops both the left and right side of the body, and therefore the brain too. It can also help in recovery after injuries or illness by strengthening the body and keeping a positive and focused mind set.
Then there are the basic aspects of self defense. Basic, because nothing is better than avoiding a fight in the first place, either by talking your way out of it, or not being there at all. But for those (hopefully) rare times that these options are not available, there's karate. Regular training shows you your physical limits, extends them, and gives you some tools and tricks to use with these extended limits.
The training is more rigorous than for children because firstly, adults are more capable of extending themselves intentionally, and of course, because there exists the option for full-contact fighting. While not for everyone, some people very much enjoy fighting full-contact fighting because it provides them with a further challenge beyond the dojo (training hall).
For others, the appeal may be more in doing kata ( form ) , a prearranged pattern of fighting moves that require both power and grace, and are said by some to be the foundation of fighting skills.
Whatever your reasons and goals are , practicing Karate can help you become stronger, healthier and a better human being.