Loosely: gravity is the force attracting masses so "repel gravity" makes no sense. Forces may be repulsive, but you cannot repel forces.
You'll see that with electromagnetic charges, like charges repel ... whereas, if we treat mass as the gravitational charge then we see like charges attract (and we only ever find positive charges).
This, I suspect, is the idea you have come across.
All this means is that it may not be useful to think of gravity as a force like the electromagnetic force between charges.
(This is pretty much the standard way to understand gravity: as a pseudoforce arising from geometry vaguely analogouse to centrifugal force arising from rotation. A negative gravity would be like postulating an inwards-pointing centrifugal effect.)
Still, there is quite a lot of discussion about a possible physical basis for antigravity ... ie. see "cosmological constant" and "exotic matter".