Among the people of the Westlands, Delving is the act of "feeling around" with the One Power to look for injuries and illnesses. This is often used directly before Healing. The ability to Delve, and discover an illness or injury, does not necessarily mean one possesses sufficient Healing ability to cure it. Verin Mathwin thinks that she is unsurpassed at Delving. Nynaeve al'Meara also seems to possess this ability, allowing her to detect compulsion placed by Graendal on Lord Piqor Ramshalan, which allows Rand al'Thor to discover Graendal's hideout. Also, Nynaeve uses this to detect the madness of Naeff, Jahar Narishma, and Damer Flinn.
Among the Seanchan, Delving refers to the use of the Power by damane to search the earth for metal ores and such, and to extract the ores from the ground. This is a greatly sought-after ability for the Seanchan and damane who possess this Talent are highly prized.
It is thought that this was the traditional meaning of Delving, however as very few women have the talent, let alone sufficient strength in Earth, to perform this type of delving and the meaning has changed to mean to the talent described above. A reason for this could be that very, very few damane are used for healing due to their nature as possessions in Seanchan society.