The critical path method (CPM) is a project scheduling technique developed in the late 1950s. It consists of modeling a project as a network of tasks linked by dependencies, then computing the longest chain of sequential tasks: this "critical path" determines the minimum duration of the project.
In practice, for each task you compute its earliest and latest dates (through a forward then backward pass over the network), which reveals its float (slack). Tasks on the critical path have zero float: any delay on one of them pushes back the project end date by the same amount. Conversely, a task with float can slip within a certain limit without affecting the final deadline.
CPM is valuable for prioritizing: it shows where to focus attention and resources, and which tasks to watch first when the schedule comes under pressure. It is almost always used together with the Gantt chart, which provides its visual reading, the critical path often being highlighted in a dedicated color.
In eyeot's Projects module, the critical path is recomputed from task durations, their dependencies (finish-to-start, start-to-start, finish-to-finish, start-to-finish) and their lags, in order to bring out the chain of zero-float tasks that fixes the end date. Tracking schedule variances is then extended through earned value management.