Deficit spending is when a government doesn't have the funds to pay for programs and takes out loans to cover the expense.
You can think of deficit spending this way: if you know you'll make $100 next month at your part time job, and you plan to buy new sneakers that cost $150, your personal deficit spending will be $50. You'll have to borrow that amount to cover the shoes. It's the same for governments, which sometimes use deficit spending, borrowing to cover a lack of revenue. The Latin root of deficit is deficere, "to fail or be deficient."