1. Literally, to be very quick at drawing one's gun in readiness to shoot it. The gunfighter was so fast on the draw that he often shot his enemies before they reached their own gun.
2. By extension, to be able to understand, anticipate, or react to a given situation or circumstance very quickly. Faced with criticism by environmentalists, the company's PR rep was fast on the draw to point out its important role in job creation for the local community.John's always a little too fast on the draw to defend his country's role in the war.You have to be fast on the draw if you want to get ahead in the world of business.