"Stay" is a pet command that tells the pet to remain where it is while the pet's master (a hunter or warlock) moves away. A defensive pet will still attack if something attacks it; and an aggressive pet will still aggro any mob that comes too close.
The Stay command can be used by hunters to flee combat. This is done by ordering a pet with aggro on a mob to stay, then running until the pet is unsummoned; if done correctly the hunter be out of the mob's aggro range by the time the pet disappears. So long as the pet survives, it can be immediately resummoned with the Call Pet ability.
Stay can be used in combination with Attack and Passive to temporarily clear a quest object or gatherable resource. For the best results, station the pet (Ctrl+3 by default) as far from its owner as possible. Then, order the attack (Ctrl+1) on the object-guarding mob. As soon as the mob targets the pet, order a retreat (Ctrl+0) and run in yourself! Some objects (e.g. chests) cannot be obtained this way.