An Anbo-jyutsu arena aboard the Enterprise.
Anbo-Jyutsu was a type of Human martial arts.
It took place in a circular arena, where two opponents would compete against each other. Both competitors wore light protective armor and a helmet that had a solid visor, which effectively blinded the competitor. A staff was used as a weapon, with a proximity sensor on one end and a small spherical cushion on the other. With the help of the proximity sensor, a player could detect, by means of an audio signal, where his/her adversary was.
Commander William Riker used this game in 2365 as a means to settle long-held grudges against his father, Kyle. (TNG: "The Icarus Factor")
Kyle Riker considered Anbo-Jyutsu to be the ultimate form of Human martial arts.
Background
The writing on the ring seems mostly decorative and not very meaningful.
The large character in the center (星) 'Hoshi', means "star" or "mark"
The words next to 星, in katakana are:
(ラム) 'ramu' "lamb/ram/rum" and (アタル) 'ataru' "To confront"
On the ringside ('mizu' and 'hi' are also on the armor)
(水) 'mizu' "water" (火) 'hi' "fire" and (ユリ) 'yuri' "lily"
The Japanese spoken by the Rikers during their right in this ring is somewhat poorly pronounced. What they most likely were trying to say was 'Yoroshiku, onegaishimasu' which, in this situation could be taken to mean "Well met, please do your best." When knocked to the ground the competetors would shout 'Matte!' which means "Wait!"
It could be theorized that this sport is an evolved form of the Japanese martial arts, since competitors speak Japanese phrases before, during, and after a match.
It has popped up in a few instances in Trek literature: Will Riker spars with Christine Vale in A Time to Love, and B'Elanna Torres with Kes in Distant Shores.