Delayed Hyper Combo (DHC)

DHC itself isn't a glitch; it just involves canceling one character's Hyper move animation into a second character's Hyper by inputting the commands for the second character's hyper (for example, Quartercircle Forward + 2 Attack buttons). The first character's Hyper will abruptly be canceled into the second character's Hyper. There's a time window when you can do this, usually around before the final hit in the first Hyper combo. Note that not all Hypers DHC into eachother cleanly; some will almost always miss when chained together.

The DHC "glitch" is something different from DHC itself; a DHC is a completely intended gameplay mechanic (which is used in other games such as Skullgirls). The DHC glitch involves using a DHC move that you're sure will miss, which will end your combo/hitstun in order to reset damage scaling. I'm not sure it's really a glitch, it's just a peculiar sort of Reset used to reset damage scaling (it's been removed in Ultimate though, so maybe it was a glitch). I can't word it much better than Chacronic in this GameFAQs thread:

When you use a hyper then tag in someone else for another hyper combo aka a DHC that will deliberately miss (Think Taskmaster/Wesker's counters or Wolvies Beserker charge hyper combos) so you get a reset in damage and can start up a new combo. This will usually result in far more damage then just doing a delayed hyper combo and usually killing an opponent in a single combo string.

Here's a video of it:

Note that the DHC reset trick was removed in Ultimate Marvel vs Capcom 3 so it might have been a glitch afterall. Either way it's MVC3 only.