Brazilian Jiu-Jitsu is a martial art consisting of throws and take downs to bring your opponent to the ground where you can control them using leverage or submit them using chokes and joint locks.
Once a fight is brought to the ground 80% of dynamic striking has been taken out of the equation. A practitioner can train Brazilian Jiu-Jitsu for multiple reasons whether it be for self defense, competition, or fitness.
Gi Jiu-Jitsu
When the martial artist is wearing a traditional kimono/uniform
NoGi Jiu-Jitsu
When the martial artist is wearing shorts and a rash guard instead of the traditional kimono