An unsecured debt is a debt that is not held against any collateral. If the borrower defaults on the loan, the lender has no collateral to take/repossess, and therefore no security on the debt.
Credit cards are a good example of debt with no security. If you don't pay your bills, there's nothing for MasterCard or Visa to come and take from you to even things up. Instead, they have little alternative but to hire collection agencies or pursue civil remedies, both of which ultimately cost the lender money, and cost other borrowers higher interest accordingly to make up for it.
Unsecured loans are generally charged at significantly higher interest rates, because they have a larger percentage of bad debt that must be accounted for, and interest is adjusted accordingly to keep profits where the lender wants them to be.
Other examples of unsecured debts include:
