Priority debts are debts to the IRS, your state taxing authorities and child support and spousal maintenance/alimony arrearages. These debts typically must be paid off in a bankruptcy or will not be discharged.
Secured debts are debts that have some sort of collateral securing the loan. For instance, your car is the collateral for your car loan and your mortgage is secured by your house. Sometimes certain stores credit cards have a clause in the application wherein you pledge the assets you are buying as collateral. If so, the debt would be secured. Typical examples are jewelry store credit cards, electronics store credit cards and computer manufacturer credit cards.
Unsecured debts have no collateral securing the loan. Credit cards are a good example of unsecured debt. Student loans are also unsecured but, under the current law, student loans are very difficult to discharge in bankruptcy..