What is the Critical Path Method (CPM)?

The critical path method is a step-by-step project management technique to identify activities on the critical path. It is an approach to project scheduling that breaks the project into several work tasks, displays them in a flow chart, and then calculates the project duration based on estimated durations for each task. It identifies tasks that are critical, time-wise, in completing the project.

CPM = project complexity and plan how to achieve required end result.

CPM is a project management technique that analyzes what activities have the least amount of scheduling flexibility (i.e., are the most mission-critical) and then predicts project duration schedule based on the activities that fall along the "critical path." Activities that lie along the critical path cannot be delayed without delaying the finish time for the entire project.

In another meaning, any delay in activities that belongs to the CP will lead to a delay to the project... That's why it's called critical!

The long path in the project and all activities in this path not allow to float

The Critical Path Method (CPM) is one of several related techniques for doing project planning. CPM is for projects that are made up of a number of individual "activities." If some of the activities require other activities to finish before they can start, then the project becomes a complex web of activities.

CPM can help you figure out:

• how long your complex project will take to complete
• which activities are "critical," meaning that they have to be done on time or else the whole project will take longer

If you put in information about the cost of each activity, and how much it costs to speed up each activity, CPM can help you figure out:

• whether you should try to speed up the project, and, if so,
• what is the least costly way to speed up the project.

The critical path method (CPM) is a project modeling technique developed in the late1950s by Morgan R. Walker of DuPont and James E. Kelley, Jr. of Remington Rand.Kelley and Walker related their memories of the development of CPM in1989.Kelley attributed the term "critical path" to the developers of the Program Evaluation and Review Technique which was developed at about the same time by Booz Allen Hamilton and the U.S. Navy. The precursors of what came to be known as Critical Path were developed and put into practice by DuPont between1940 and1943 and contributed to the success of the Manhattan Project

is the stepwise project management techniques  in planning process that aim at preventing process shortcoming 

CPM is a method in project time management. When you sort activities and create activity network diagram, then you specify required time to each activity and possible time float for that activity.

In your network you will find a path (from start to finish the project) that no float is permissible through that (called Critical Path). Any change (increase) in time for activities located on Critical Path causes postponding project finish date. 

each assignment has got it own CPM to use, so depends on what is on the table.