The critical path is the longest sequence of dependent tasks in a construction schedule, end to end. Its total duration is the project's minimum possible duration. Tasks on the critical path are called "critical" because any delay to them delays the entire project.
Identifying the critical path is the core of construction scheduling. It tells the project manager which tasks require the most attention and which have float (slack time) that allows scheduling flexibility. On commercial TI work, the critical path often runs through long-lead procurement (custom millwork, specialty equipment, structural members), MEP rough-in coordination, and inspection windows. Compressing the schedule means accelerating critical-path tasks specifically; accelerating non-critical tasks does nothing.