Clairvoyance allows you to map an area of the dungeon around you, showing corridor walls and stairs. This is similar to magic mapping but somewhat limited. Where magic mapping reveals the whole level, if it can be mapped, Clairvoyance will only reveal a 19×11 region around you. Like magic mapping, the map will remain unlit and will not reveal secret doors, traps or objects. Importantly however, Clairvoyance will reveal the map surrounding you on levels that will not be mapped by magic mapping, such as the Valley of the Dead.
If you have Clairvoyance as an intrinsic or extrinsic, the effect of mapping the area around you is not constant but will occur with 50% probability every 15th turn.
A time when clairvoyance may be undesirable is when exploring a maze, because it makes it difficult to distinguish areas that have already been visited from those that haven't (and therefore may contain useful objects).
You can only ever get intrinsic Clairvoyance temporarily, for a random length of between 500 and 999 turns, by donating between xplevel*200 and xplevel*400 to an aligned priest.
In SLASH'EM, a blessed potion of clairvoyance will give you intrinsic clairvoyance for between 100 and 149 turns.
In SLASH'EM, you can also get a single application of clairvoyance by drinking an uncursed Potion of Clairvoyance.