Someone who is diligent works hard and carefully. If you want to write the epic history of your family, you'll have to be very diligent in tracking down and interviewing all of your relatives.
Diligent comes from the Latin diligere, which means "to value highly, take delight in," but in English it has always meant careful and hard-working. If you're a diligent worker, you don't just bang away at your job; you earnestly try to do everything right. Although being lucky and talented doesn't hurt, it's the diligent person who eventually succeeds.