Definition
The chain of linked activities that determines the total project duration: it has no float, and one day of delay on any of its activities delays the whole project by one day.
In detail
The critical path answers where to compress: making anything off the path faster does not move the delivery date. The three common phrasings are the same thing — the chain with no float, the longest-duration chain, the longest path through the project. It shifts as the project progresses, so it must be recomputed rather than drawn once at kickoff. Beware the same name elsewhere: in FAST functional analysis for value engineering the critical path means the functions between the two scope lines and has nothing to do with schedule, so the two must not be applied to each other.
Example in practice
A project runs 26 days and the team finds the bottleneck in the purchasing chain. Compressing design reviews off the path changes nothing; ordering long lead-time parts early cuts the duration to 20 days, and the critical path moves to the pilot validation chain.