"Choker tournament" is often just another name for Money Ball, Devil Ball, Pink Ball, Yellow Ball, etc. All use the same basic premise.
Let's say our tournament is a 4-man Choker. The players are A, B, C and D. On the first hole, Player A is the choker - he plays alone. The other three - B, C and D - play as a team. At the conclusion of the hole, Player A's solo score and B-C-D's score are added together to create the team score. The three members on each hole who are playing the team ball might be playing any number of formats; they might each play their own ball and count the one low score; they might be playing a scramble. If it's a 3-man Choker, then the two players teaming on each hole might play alternate shot. There are options, in other words.
In choker tournaments, a common variation is this: All team members tee off on each hole. The best drive is selected, and the golfer who hit it becomes the choker. He completes the hole solo. The other team members play scramble into the hole, with their scramble score combining with the choker's score.

