Precedes

No: it means "comes before" in an ordering defined nearby. Mathematicians use ≺ when they want to order things that are not plain numbers: sets, words, tasks, vectors, events. The text usually says something like "we write a ≺ b if…" and that definition is the meaning.

Using a separate sign keeps two orders apart on one page: < can still mean ordinary numeric less-than while ≺ means the special order. Read a ≺ b aloud as "a precedes b". Its mirror ≻ reads "succeeds", and the version with a line under it, ≼, allows equality as well.

Where will I actually see it?

Mostly in maths, economics and computer-science texts. In economics, x ≻ y says a person strictly prefers x to y, so y ≺ x says y is less preferred. In order theory, ≺ is a common name for a strict partial order, where some pairs may not be comparable at all.

Other established uses: majorization of vectors (x ≺ y) in inequality theory, the ordering of matrices in optimization, and "happened before" orderings of events in distributed computing. Each text states its own definition, so check it.