The critical path is the longest chain of dependent activities through a project schedule — and therefore the one that sets the finish date. Activities on the critical path have zero float: if any one slips, the whole project's completion slips with it. Activities off the critical path have slack.
Critical Path Method (CPM) scheduling is how PMs and schedulers find and protect that chain. Knowing what's critical tells you where to focus — accelerating a non-critical task wastes money, while a day saved on a critical task is a day off the whole job. Long-lead procurement usually lives on or near the critical path.