When a country borrows money in order to fund public spending is incurring into a deficit situation, because the total amount due exceeds the total income generated in a specific time period. Therefore there is deficit spending.
The interest is the price to be paid for the borrowed funds. It is a percentage applied to the total loan amount (called the principal), accruing a quantity that will have to be repaid, together will the principal, to the lender, following a repayment schedule that is usually predefined.