MMA is an acronym for “Mixed Martial Arts” and can either refer to a sport or “style” of martial arts training. In the United States, it most resembles boxing in that it’s widely practiced as a form of combat sport in a gym setting (as opposed to “dojo” or similar setting, characteristic of traditional martial arts) and that it is also a sanctioned sport with a ruling body.
The use of the word “style” may seem misleading to some, as MMA has combined elements of what works from various styles (wrestling, boxing, jiu jitsu, muay thai, etc) into a single system of fighting both on the feet through various strikes and clinches as well as on the ground, where opponents will jockey to implement strikes, submissions, escapes or to gain dominant position. Nevertheless, at this point MMA has been taught on its own in a manner where many simply see it as its own “style” or “system” without the need to regard the specific systems from which many of these techniques originally come from.
The UFC (Ultimate Fighting Championship) is the most well-known organization and features most of the top-ranked fighters. The first UFC aired in 1993 where fighters of various disciplines (including Brazilian Jiu Jitsu, Karate, Savat, Boxing and Sumo) would gather for the chance of winning an 8-man tournament and paycheck. It was quickly realized that:
From these realizations, MMA would gradually evolve into what it is today, where fighters are well-rounded, often to the point of being known for their new adaptation to MMA as opposed to their root style (ie. grapplers with impressive striking skills, or muay thai-based fighters with impressive ground games).
The UFC rules also evolved along the way. Early fights allowed for hair pulling along with punches/kicks to the groin. This would be banned along with certain elbows from certain positions, along with kicks to the face against an opponent on the ground.
Other notable organizations include Bellator and World Series of Fighting.
While UFC would popularize MMA (dubbed “No Holds Barred” at first), it hardly marks the origin of what we would call MMA. In the US alone there already existed smaller events (though largely underground). But the earliest recording of an event closely resembling what we call mixed martial arts dates back to the ancient greek art/event known as Pankration.