Government spending in excess of what they take in as tax revenue.
Don't confuse the deficit with the debt: the debt is the total amount the government owes; the deficit is the annual amount by which the debt gets bigger... and bigger:
|U.S. Debt (as of early 2003) ||$ 6,400,000,000,000|
|Projected Deficit for 2003 ||$ 300,000,000,000|
|Distance to Pluto||3,000,000,000|| mi|
"Running a deficit" is sometimes proposed as a short term economic stimulus (Democrats tend to mean an increase in spending, Republicans tend to mean a decrease in tax rates); but the after-effects can be a long term drag, either in the form of an eventual tax increase or higher interest rates to cover the increase in government debt.
See the government spending diagram.
You can get information on the deficit from the Congressional Budget Office,
and on the debt from the Treasury Department.