The “roll” is a system highly characteristic of the King of Fighters series, where it is called an “Emergency Evasion”. It is not always a literal roll, but the mechanics are essentially the same.
It appeared in KOF ’96, where it replaced the Attack Avoidance, much as the dash replaced the frontstep in the same game. Contrasted with the dash/step systems, however, the Emergency Evasion is a primarily defensive system like the Attack Avoidance it replaces; even though it allows temporarily safe and somewhat quick movement, the defensive aspect is the main point.
Many other games have some sort of “roll”; less often as a system, more often as moves on a specific character that allow the same capabilities to them alone (or in Hibiki Dan’s case, to parody SNK, since this is a characteristically SNK system).
The Emergency Evasion, or roll, moves either forward or backward while being invincible to strikes and projectiles (usually doing a somersault, hence the “roll” nomenclature). While moving, it is possible to pass through the opponent and end up on the other side of them (i.e., no touch hitbox calculation).
The command is AB for a forward roll and + AB for a backward roll (except in KOF ’96, where the command is AB for a backward roll and
+ AB for a forward roll).
The roll is good for invalidating unblockables and other things that would be awkward to defend against otherwise (e.g., a properly considered guard-cancelled roll or Blow-Off [CD] Attack can often save you from a chip K.O.), and allows you to try for some comparatively easy stuffing.
However, the roll is defenseless against throws, and leaves you open at the end for a little bit. Among other reasons, this is why throws are comparatively powerful in KOF compared to other series (and is certainly one of KOF’s peculiarities).