In NetHack, telepathy is an intrinsic usually gained from devouring the corpse of a floating eye. It is only functional while you are blind, which is why wizards often start out with a blindfold, and towels are such handy items.

Telepathy allows you to know the position and type of all sentient creatures on the level. Non-sentient creatures, such as the undead and slimes, jellies, or molds cannot be "seen" in this manner. Golems and similar creatures cannot be "seen" either, as they aren't actually alive.

Of all the intrinics you can have in NetHack, telepathy is by far the most useful and should be acquired as soon as possible. Certain deadly creatures, notably eels, cannot normally be seen (they are underwater) and will ambush you fatally unless you use telepathy. Also, invisibility becomes much less dangerous if you are telepathic.