The critical path is the longest chain of dependent activities through a programme: the sequence with no float, where any delay flows directly into the completion date.
It matters because delay only earns an extension of time if it affects completion, which usually means showing the affected activity was on, or became, the critical path. Activities with float can slip without moving the end date.
The critical path is dynamic: as work progresses and sequences change, it moves. Good delay analysis therefore relies on programme revisions and contemporaneous progress records that show where the path actually ran at the time of the event.