Strictly speaking, it doesn’t necessarily do anything.
If a Makefile has a target named check, then make check will “build” that target. It’s typically a phony target, meaning that it is a make-scripted command rather than a file named “check” that gets created.
The gnu project advises that all gnu software should include a make check target that runs post-build tests in the build directory, so make check can be used frequently on packages distributed from the FSF. Other projects will sometimes follow this convention as well.