A Hyper Combo is a powered-up special attack used by characters in the Marvel vs. Capcom series.
They differ from Super Combos in that they have easier inputs; they only require a single special move motion plus two attack button presses (which is more similar to how EX special moves in more recent Street Fighter games are performed), as opposed to Super Combos in the Street Fighter series, which require two special move motions plus a single punch or kick button.
Some Hyper Combos, such as Zangief's Ultra Final Atomic Buster, cost three power bars to perform instead of one. From X-Men vs. Street Fighter to Marvel vs. Capcom 2, those instances were rare, but they were made more common in Marvel vs. Capcom 3, where almost every character has a Level 3 Hyper Combo. Starting in Marvel vs. Capcom 3, with the transition to 3D character models, during Level 3 Hyper Combos, the camera would break from its normal fixed position to show a more dynamic, cinematic view of the gameplay, similar to the Ultra Combos in Street Fighter IV.