Unweaving is the ability to pick apart a weave, rather than letting it dissipate naturally. Aes Sedai and Windfinders both believe that to do so is dangerous and it should not be attempted (TPoD, Ch. 3) and even in the Age of Legends, they thought it impossible (TPoD, Ch. 2). The Wise Ones, however have learned the skill and believe it is simple as long as a person does it correctly (TPoD, Ch. 3), makes no mistakes and does not stop or let go of any threads, which become slick and hard to handle (TPoD, Ch. 6). Mistakes however, can have very serious and unexpected consequences (TPoD, Ch. 6), which could range from a loud noise or flash of light, to an explosion killing everything with a hundred yards, or burning out everyone close (TPoD, Ch. 6).
Aviendha unweaves a gateway when she sees Moridin watching them, as she doesn't want any of the Forsaken to be able to read the residues if it dissipates naturally and so follow them. Elayne does the same when they flee the farm when the Seanchan attack, as she doesn't want them to learn how to Travel. Moiraine also does something to cause the residues of a weave to dissipate, but it is not known if she unweaves it or merely uses some other weave to disperse them (TEotW, Ch. 49).