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.
Float is what makes the concept useful and what makes it contentious. An activity with two weeks of float can absorb a week of delay without affecting completion, so a delaying event that hits it may cost real money without earning any extension of time. Contracts and disputes then turn on who owns that float: whether it belongs to the contractor who planned the sequence, to the project as a whole, or to whoever happens to use it first. Standard forms answer this inconsistently and amendments often change the answer.
The other complication is that delay rarely arrives one event at a time. Where an employer-caused delay and a contractor-caused delay run over the same period, the analysis has to deal with concurrency, and different methods produce genuinely different answers about entitlement. This is a large part of why delay disputes are expensive: the parties are frequently arguing about method rather than about facts.
What settles most of it is the quality of the progress data underneath. Every method of delay analysis, whatever its label, needs to establish where the works actually were on given dates. Where that comes from consistent daily records the analysis is an exercise in interpretation. Where it comes from photographs, memory and a monthly report it becomes an argument about the evidence itself, which is a much worse place for the party carrying the burden of proof.
Establishing where the path actually ran starts with daily progress records: see the kind of daily record Construction Metric builds automatically as the job runs.