A sonic screwdriver is a multi-purpose tool used by the Doctor that uses sounds waves to manipulate matter, such as in the case of unlocking doors, manipulating electronic circuitry, and, every once in a while, unscrewing a screw.
The sonic screwdriver was invented by the Doctor one night after not being brave enough to kiss someone he liked. ("A Christmas Carol") It was suggested that having a lot of shelves to put up was also an influencing factor in the screwdriver's creation. ("The Doctor Dances")
For more information, see Tardis:Sonic screwdriver.