Pas de chat means simply the step of the cat.  Relatively speaking, pas de chat is a more modern step in the ensemble of ballet history.  Generally speaking, the steps became larger and bouncier as time went on.  As late as 1895, there is no trace of this now common step in the Dictionnaire de la danse by G. Desrat, which is a very detailed guide delving into the history, theory, practice, and bibliography of dance.

Our modern translation of pas comes from the common usage.  Un pas is a step of the foot or a figurative step.  In ballet pas is slightly more complicated as it indicates the ensemble of small movements that make up a "step," as we now call it.  In other words, pas de chat is not a single movement but an ensemble of movements.  Chat means cat, as in your ordinary house cat.

Pas de chat is pronounced [pɑ də ʃa].  Pas is pronounced like "pa" in the first syllable of the English papa. De is pronounced like you're practicing the sound a D makes in English.  And chat - sounds like "sh" and "ah" put together.  Resist the American temptation to add a W sound to the end of chat. 

Pas de chat is a bounding movement often performed in petit and grand allegro and is similar in movement to the pounce of a cat.  Beginning in a crossed position (3rd or 5th), the dancer performs a demi plié, the leading foot pulls up and through retiré as the dancer springs off the supporting foot.  The supporting foot also pulls up and through a retiré position allowing both feet to be lifted underneath the dancer in a retiré position simultaneously.  The first foot to lift is also the first foot to land in demi plié and the second foot follows the first back into a crossed position in demi plié.

I've heard several different explanations of cat imagery associated with pas de chat.  The two most frequent are that the thighs in mid-jump create the arched back of an angry cat and that the jump itself is similar to the pounce of a cat.  I've always preferred the imagery of a pounce.  The initial plié representing the low twitchy preparation of the cat, the up and over the cat's flight through the air, and the landing the success of the attack.  I often imagine the landing plié as the cat's effort to keep that little mouse under its paws.

See the videos below for the physical similarities between the dancer's pas de chat and the pounce of the cat.