Final answer:
The opponens pollicis muscle is responsible for the movement that allows the thumb to touch the tips of the other fingers, and it is significant for grasping objects.
Step-by-step explanation:
The muscle in the hand responsible for drawing the thumb across the palm to touch the tip of any finger is known as the opponens pollicis. This muscle is one of the thenar muscles, which are intrinsic muscles of the hand that support precise movements such as typing and writing. The opponens pollicis plays a critical role in the opposition movement of the thumb, making it possible to grasp and hold objects.