At the start of a project you map out all the activities involved and the sequence in which they occur.
Adding durations to the individual activities and appropriate links between them enable you to see how long tbe project will take.
It also allows you to see the critical path through the activities. Any delay in the critical path activities will have a direct effect on the end date of the project.
The problem comes when people concentrate purely on the critical activities and ignore less critical activities.
A sequence of (previously sub critical) activities may have only had 1 week of "float", I.e. "free" time, before they, in turn, would form the new critical path through the project. A delay of 3 weeks in such a previously sub critical series of activities would cause a 1 week delay to the project, unless the schedule is reassessed and, say, overtime used to reduce subsequent activity durations to bring the project back on schedule.
So. You not only have to keep an eye on the critical path activities, but on all others that could potentially go critical.