A grace period is the period from the date a statement was prepared by the issuer (statement date) to the payment-due date. No interest will be charged if the whole balance is paid by the end of the period. These interest-free grace periods typically last 25 days, but 20-day periods are becoming more common.
When you're looking for a credit card, avoid cards that don't offer a grace period, because you'll end up paying interest immediately upon purchase. It pays to search for a card with a longer grace period, because the amount of time you have interest-free affects how much interest you'll end up paying overall.