To place a thing under a named class. Classifying is a claim spoken over a thing, and it can be wrong about it.
Latin classis (a class, a division, a fleet) + French -fier, from Latin facere (to make); to classify is, at the root, to make something into a class-member.
The thing itself does not consent to a label and does not change shape to fit one — classifying speaks a claim over something rather than uncovering a truth already inside it, and the claim can miss regardless of how confidently it was spoken.