Understanding a formula

I built the attached vacation planner directly from the Excel Gantt Chart Template. It works great but I don't really understand how it works.
The red cells are from a conditional format with the rule "=plan", and "plan" is a dynamic named range which refers to another named range "periodinplan".
I think that the concept is genius but I would like to better understand how it works.

In addition, I would like to add a formula in H1 to count the number of people on vacation on any day.

Thank you all for your continuing help.

Thanks for the formula, works great. The day of the year is because I took the whole thing from the Excel Gantt Chart template and it used periods rather than dates. I normally keep Row 4 and Col C hidden.
I have attached the template that I based this on. I thought it pretty clever because there are no macros or formulas used, only Named Ranges and Conditional Formatting.
The formulas in my file are to convert dates to periods.
Thanks

Thank you. I love the beauty of simplifying an overly complex problem.
Your solution helps me to be able to use the concept in other ways (though I still don't understand how the original template works).