The concept of a unit period is spelled out in Appendix J of Reg. Z. As Ralphie MITCH indicates, one UP is however much time passes from one payment to the next--for most bank loans, one month. For good business reasons and customer service, most installment lenders schedule a first payment that is more or less than the normal payment period. Usually referenced as "odd days", this one odd period puts the borrower on the desired cycle--regardless of when the loan is originated.
The APR calculation is as sensitive to the passage of time as to the dollar amount of Finance Charge, so APRWIN accepts any pair of dates and crunches them (according to the Appendix J rules) into whole UPs and odd days. It also allows you to enter these values directly, if you know them.
After the first payment period APRWIN will default to uniform payment periods unless you override the UP/odd-day values it has predetermined. You would only need to override if your loan is scheduled to have "odd days" in more than the first payment period. The only good example of a loan product with multiple odd days would be a "school teacher loan" which has built-in skips during summer months.