The phrase suggests proficiency in tasks requiring fine motor skills and attention to detail. You must be good with your hands to assemble those intricate model airplanes.
Pro Tip 2/3
Complimentary
It's often used as praise, acknowledging someone's dexterity or ability to fix things. Everyone says that the new mechanic is really good with his hands.
Pro Tip 3/3
Non-Professional
Used for skilled tasks, but doesn't always mean professional training is involved. Although not a professional, my neighbor is good with her hands and made her own patio.