The pros of using a debit card over cash or check means that you can checkout at the stores faster instead of standing in line counting out cash or writing a check.
You can just swipe the card and pay for the purchases and be on your way faster.
You also avoid overdraft of your checking account when using your debit card instead of a check since with a debit card the funds must be available for the transaction to complete and if not the debit card transaction will be declined.
Cons of a debit card is that it won't help build your credit like a credit card will and if you lose the debit card you won't be able to make purchases in the event you don't have any cash on hand or checks.