This is a term that I occasionally hear used in great dramatic tones to impart a sense of urgency to the listeners. Sometimes coming from people with a background in project management, and sometimes not.
Critical Path Method comes out of project management theory, developed in the 1950s at Dupont. The concept was developed to help in the planning phase of project management, and it’s often visualised with a Gantt Chart (which predates CPM).
This helps to visualise tasks that are dependent on each other throughout a project, and the tasks that must be completed on time in order for the project to be deliverd on time are coloured red (as shown above).
These tasks are the critical path.
I suspect that most people use to refert to tasks that did not start out on the critical path, but have become critical because someone hasn’t completed their non-critical task on schedule.