You're at the (off-leash) dog park with your pup – the sweetest, gentlest canine to ever grace the earth. Free of her leash, she daintily skips up to the biggest, meanest-looking dog at the park, a bruiser that outweighs her by at least 80 pounds.
You hold your breath. She bows in front of the bruiser and the two go off galloping around the park, the best of friends.
That "play-bow" is powerful stuff! As a matter of fact, the play-bow is a canine diplomatic protocol that most dogs understand. When a dog (or wolf) invites another to play, they bow with the front paws outstretched and the hind end raised. The dog may also wag his tail and bark. This signals that what follows – chasing, light nipping and lunging – is done only in fun and should not to be taken seriously.
The dog may also exhibit a play-smile, in which the lips are pulled back horizontally. The important part of this signal is that the teeth are not bared (baring teeth is an aggressive signal).
The play-bow probably evolved out of a submissive crouch, but the signal has become an unmistakable way to indicate a desire to play, no matter where the dog is in the social hierarchy. A more dominant dog may even allow himself to be chased in the interest of fun, may encourage play by lying down and allowing a subordinate dog to "attack" him.
However, it is interesting to note that dominant dogs are not as successful in soliciting play. A general sense of aloofness may be part of the reason. Or perhaps they come across as insincere when they invite another dog to play.
Under-socialized dogs may not understand the play-bow, or know that all actions following the bow are meant in fun. Instead they may feel threatened and may bite. Fortunately, most dogs do understand dog diplomacy. It would be nice if the leaders of nations recognized friendly, non-threatening gestures so well.