The maneuver is called a "breakaway maneuver" or simply a "break", it's also sometimes colloquially referred to as "peeling off" in the context of aircraft leaving formation. You can see it more clearly in this video:
This is a standard maneuver used when disengaging from a intercepted target, or as a way to safely exit formation flight ensuring that the departing aircraft is clear of the rest of the formation group.
It also has tactical advantages as seen in the photo you posted (when being tracked by an infra-red/heat-seaking missile, dropping flares and a hard breakaway is one technique used to convince the missile that the flare is actually your engine, by getting your real heat source out of its "line of sight" quickly).
Aerodynamically the breakaway maneuver is nothing more than a steep turn: Roll the aircraft into the desired bank, setting power and pitch up to maintain your altitude and airspeed in the turn as desired.
A Cessna 152 flying in formation could break away using the same maneuver, though the bank angle and airframe loading (G forces) would need to be maintained within the aircraft's limitations.
The primary difference with fighters and attack aircraft is that the bank angle is dramatically steeper (in the extreme, a 90-degree "knife-edge" bank) and the turn much tighter because these aircraft have the excess power (thrust) required to sustain flight in that configuration and are sturdy enough to withstand the G loading induced by a "hard pull" in the breakaway maneuver. The abrupt wings-up turn along with the nice roar you get advancing the throttles makes the maneuver an impressive one for airshow crowds to watch.