This page contains information regarding Star Trek: Lower Decks, and thus may contain spoilers.
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.
Riker used this game in 2365 as a means to settle long-held grudges against his father. Kyle considered anbo-jyutsu to be the ultimate form of Human martial arts. Katherine Pulaski considered it highly dangerous.
The move called Hachidan kiritsu was illegal in the 24th century and would give a competitor using it an unfair advantage. When Will turned twelve years old, Kyle knew he could not defeat him by conventional means, so he began defeating his son with this move, until as an adult, Riker discovered his father had "cheated " him. Kyle defended his attitude by explaining he had to keep the boy interested in anbo-jyutsu by not letting him win. (TNG: "The Icarus Factor")
Beckett Mariner was a master at anbo-jyutsu. She once fought a match against Brad Boimler and Sam Rutherford on the USS Cerritos in 2381, and defeated them one-on-two. Over the next three months, Boimler and Rutherford practiced secretly at midnight, hoping to best her on their next match. However, when they faced her again, she soundly trounced them both once more. (LD: "Mugato, Gumato")
"AN-bo JUT-su" was the pronunciation for this martial arts' name, according to the script pronunciation guide for "The Icarus Factor". 
This sport was derived from Japanese martial arts. Evidence of this is that competitors speak Japanese phrases before, during, and after a match. The fight between the Riker father and son was devised by Robert L. McCullough, who was credited with co-writing the teleplay of "The Icarus Factor". "I was studying karate, so I just used all that," explained McCullough. "I knew the karate philosophy, and I wanted them to have an ultimate confrontation and then reconcile. That's how it evolved." (Starlog, issue 187, p. 55)
The name of the sport is probably derived from Japanese 暗 (an, "darkness"), 棒 (bō, "staff") and 術 (jutsu, "technique"). So 暗棒術 (anbōjutsu) means "the martial art of staff [combat] in darkness."
The writing on the ring and armor are references to Japanese culture.
One reference is to the anime series Urusei Yatsura, the name of which is also used as the name of the SS Urusei Yatsura. The large character in the center, 星 ("Hoshi / sei", star), is used in the title. The words next to 星, in katakana are ラム ("ramu") and アタル ("ataru"), the names of the main characters. The phrases "Urusai" (うるさい, loud/obnoxious) and "Yatsura" (やつら, people) are written on the back corner, which are what the title is said to come from.
Another is probably to The Book of Five Rings, a classic martial arts text. On the front of Will Riker's armor, 地 ("chi", ground), 水 ("mizu", water), and 火 ("hi", fire) are written while on the front of Kyle's 水, 火, and 空 ("sora", sky) are visible. On the back of Kyle's helmet is 空; 水 and 火 are also on the side of the ring. These are names of four of the five chapters of the book (the missing one is 風 ("kaze", wind)).
In addition to these references, ユリ ("yuri", lily) is also written on the ringside. One banner in the corner reads 忍耐 ("nintai", perseverance).
The Japanese spoken by the Rikers during their fight in this ring is poorly pronounced. What they were trying to say from the text in the script was "Yoroshiku onegaishimasu" (よろしくお願いします, which is a standard "first meeting" phrase in Japanese which literally means "please treat me gently") which, in this situation could be taken to mean "Well met, please do your best." (Instead of the words being romanized, closed captioning says, "ceremonial chant," which is untrue.) When knocked to the ground, the competitors would shout "Mate!" (待て) which means "Wait!"
The illegal move Hachidan kiritsu, when written in kanji as 八段規律, could be translated to mean "eight-steps rule."
Costume Designer Durinda Rice Wood created the outfits of the players by using different types of motorcross suits after she saw them in a motorcross magazine. ("Departmental Briefing Year Two: Memorable Missions - The Icarus Factor", TNG Season 2 DVD special features)