The big challenge for a project manager when is starting a project is to estimate the optimal combination between time and resources needed to achieve the scope, aka to complete the project.
Critical path is the longest REQUIRED path between the begining and the end of the project.
In a project is common that many activities to occur or develop simultaneously. Such activities involve usually different teams or resources and can differ in time lengts. If a phase of a project involve for example two diffetent activities that can be completed in paralel (neither one of them depends of the other), it is a good chance that they will have different completion time. It is said then that the smaller one (in terms of time completion) will float in the time window of the other. That means that the smaller one can be started either at the same time with the bigger one, or a little bit later and still finishing at the same time or even before the bigger one finishes. If the window time allowed by the bigger activity is not exceeded by the smaller activity, the critical path and total time of the project will not be affected.
If you have only one resource that need to do all the work necessary, the critical path became egual to the sum of the length of all activities (tasks) in a project.
Real life scenario
Let’s supose a stakeholder employ a project manager to do a specific job and say something like “I have this ammount of money and I want this job done. Can you provide me an information to answer the question if this is the correct amount of money needed and what is the time needed to achieve the desired goal ?”
Ideally the project manager should be able to come up with at least a couple of sollutions to address the challenge, some of them involving an expansion of the budget, with a compensatory benefit of completion time shortening, others with a
smaller budget in detriment of time, and especially if the budget seems too low, even with a shortening of the goals of the project.
This is the meaning of project management, the capability to optimally combine the budget and time in order to achieve a specific goal.