means To pass a substance through a sieve to separate the fine from the coarse, or, by extension, to examine something carefully to pick out what's worth keeping.

from From Old English 'siftan,' to strain through a sieve — and indeed 'sift' and 'sieve' are blood relatives, both descended from a Germanic root tied to the mesh that lets the small stuff through. The kitchen sense came first; the figurative 'sifting through evidence' is the same gesture, just done with the mind instead of the wrist.