If you have stealth, sleeping monsters will not be awakened as you approach.
Stealth can be either intrinsic or extrinsic. It can be gained by wearing certain items or playing certain roles. Some characters, such as valkyries, rogues, and archeologists start out with intrinsic stealth. Monks gain it at level 5, Rangers gain it at level 7, and Barbarians and Samurai gain it at level 15.
Losing intrinsic stealth (stolen by a gremlin) produces this message:
"You feel clumsy"
"I grant thee the gift of Stealth."