Discussion Cycles measures the number of times a conversation on a pull request goes back and forth between people.
Each time a contributor comments after another contributor, the Discussion Cycle count increases by one.
Examples:
Person A comments, Person B comments, Person A comments = 2 cycles
Person A comments, Person B comments, Person B comments, Person A comments, Person A comments = 2 cycles
Person A comments, Person B comments, Person A comments, Person B comments = 3 cycles