Partial Month Charges happen when you add or remove services from your account. If you add a new service, you are billed from the first day of the new service. This means your next bill may include a full month of the new service, plus each day you had the new service before the new billing cycle began.
Partial Month Charges are determined by taking the total monthly charge and dividing it by 30 days. This is the cost-per-day of service. This figure is then multiplied by the number of days in the partial month. If the monthly charge is $30, the per day charge is about $1 per day. If you had ten days of partial month service, that would be 10 days, multiplied by $1 (per day) or about $10. (Don't forget, some months have 31 days, and then there's February with 28 days or 29 for leap year.)
Here is a sample of a Small Business Frontier bill highlighting Partial Month Charges, Promotions, and Credits.