Balefire, in the world of the Wheel of Time, is a weapon created with the One Power or the True Power (both being kinds of magic available in the Wheel of Time), described as a blindingly bright beam of "liquid light" immediately annihilating almost anything it touches.
Balefire is a weave (or ability) of the One Power or the True Power. It is a weapon which creates a beam described as "liquid light" that is capable of destroying nearly any substance. Balefire has the added effect of undoing the actions of its victims backward into the past. An example of this effect is when Rahvin, a Forsaken (one of the antagonists of the series), kills several characters but is later destroyed by Rand al'Thor using balefire. The balefire not only kills Rahvin, but removes the effects of his actions in the recent past. As a result, the slain characters' deaths are undone and they are returned to life, but with a blurred memory of their death. Others who witnessed their deaths expressed surprise at seeing them alive.
Another important fact is that it removes the victim from the Pattern completely, for example preventing Forsaken from being resurrected. Balefire has different effects based on what it hits. For living beings, a mere touch seems to be enough to wipe the entire being from existence. For normal structures and objects, it seems to destroy only what it touches (such as leaving a wall with only the portion which the beam touched removed).
Usage of balefire risks the destruction of the Pattern (the fabric of reality in the Wheel of Time universe). The stronger the balefire and the more it hits, the stronger the effect on the pattern. During the War of Power (the war which took place 3,000 years before the main timeline in the books) the forces of the light and the dark both stopped using it for fear of its effects.
Cuendillar is the only known material to resist balefire. Rand al'Thor did once part a stream of balefire with (or through) the sa'angreal Callandor in the Stone of Tear, but whether or not this is an integral quality of Callandor (or, for that matter, what The Sword That Is Not A Sword is made of) has yet to be addressed.
It is possible that the intersection of two beams of balefire can cause adverse effects in the channellers. When Rand and an unknown-to-him male channeller (the forsaken Ishamael, later renamed Moridin) used balefire at the same time and the beams crossed, both were nearly knocked unconscious by the backlash. Some regulars in Wheel of Time newsgroups consider this to have cause in temporal paradox: both men were still channelling exceptionally powerful weaves that they had never actually cast. However, this may also be because Moridin was most likely using the True Power, drawn from the Dark One, rather than saidin. It is also possible that balefire has unknown effects when performed on weaves.
In "A Memory of Light", Egwene invents a weave that counteracts and blocks balefire and can repair its effects on the pattern.
Balefire dates back in its use to the War of Power in the Age of Legends, when it was used to destroy entire cities. It is implied that the channelers of the age did not entirely understand what they had discovered, but that when they realized they were unraveling and destroying entire swathes and days of the Pattern, and in doing so threatening the very fabric of Creation itself, both sides mutually abandoned its use, on their own, with no actual negotiation needed. In the era of the novels, only the Forsaken (survivors of the War of Power), Rand al'Thor, Nynaeve al'Meara, Moiraine, and a few of their associates have access to balefire without the assistance of a ter'angreal.