To fall in small drops or to let liquid fall in drops; can also mean someone who lacks energy or character.
From Middle English dripen, from Old English drypan. Possibly onomatopoeic, imitating the sound of falling drops. The slang meaning of 'boring person' developed in 20th century American English.
The word's sound perfectly mimics what it describes - this is called onomatopoeia. Recent slang has reclaimed 'drip' to mean 'style' or 'swagger', showing how language can completely reverse a word's connotations.
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