Understanding critical path
The longest string of dependent, non-compressible tasks is the critical path.
Every complicated project is the same. Many people working on many elements, some of which are dependent on others. I want a garden, which means I need grading, a bulldozer, a permit, seeds, fertilizer, irrigation, weeding, planting, maintenance and time for everything to grow. Do those steps in the wrong order, nothing happens. Try to grow corn in a week by giving it a bonus or threatening to fire it, nothing happens...
Critical path analysis works backward, looking at the calendar and success and at each step from the end to the start, determining what you'll be waiting on.
For example, in your mind's eye, the garden has a nice sign in front. The nice sign takes about a week to get made by the sign guy, and it depends on nothing. You can order the sign any time until a week before you need it. On the other hand, you can't plant until you grade and you can't grade until you get the delivery of soil and you can't get the delivery until you've got a permit from the local town.