The phrase implies a quick, impulsive action without much thought or deliberation. He snatched at the bread, starving after the long journey.
Pro Tip 2/3
Physical Reach
It often refers to a physical movement of stretching out an arm to grab something. During the basketball game, he snatched at the ball to intercept the pass.
Pro Tip 3/3
Emotional Impulse
The phrase can convey a sense of desperation or urgency in the speaker's action. After being trapped for hours, she snatched at the rope lowered to her.