The story
From butter + fingers (suggesting that someone is clumsy and drops things as if their hands are coated in slippery butter), from butterfingered.
Etymology from Wiktionary, CC BY-SA 4.0.
Today it means: Someone who tends to drop things; (more generally) someone who is clumsy or uncoordinated; a klutz. Full definition →
From butter + fingers (suggesting that someone is clumsy and drops things as if their hands are coated in slippery butter), from butterfingered.
Etymology from Wiktionary, CC BY-SA 4.0.