Sift means to separate the fine part of a substance with a sieve. It can also be used figuratively, where it means to examine something closely.
As he talked, his wife, Setsuko, squatted in the ruin of the house. A small woman, she had a smudge of soot on her face as she carefully poked and sifted through a powdery ash, digging up wine glasses that had melted into misshapen lumps, uncovering shards of china, then moving on, foot by foot. (NY Times)
Instead, Mr Collins advocates old-fashioned management virtues such as determination, discipline, calmness under pressure and strategic decision-making based on careful sifting of the evidence. (The Economist)
The one I grew up with, “Sift two cups of flour to remove any grit, clumps, or insect casings.”
Oh! how spoiled is the modern world! Now we bring the box of already prepared pancake mix home and stick it in the freezer for two weeks, so the bugs never hatch out, and we never contemplate they are there.