If somebody trips you when you’re about to make a jumpshot, that’s interference — he’s blocking your shot. If you're running interference, you’re protecting the quarterback — you’re making yourself the obstacle between him and anybody trying to tackle him.
Governments are sometimes accused of interference in other country's affairs. If your neighbor’s in a civil war and your president sends in troops, you may be accused of interference in that country's internal affairs, even if you’re trying to provide humanitarian aid. If all you hear on your radio is static, you’ve got interference — something is blocking the clear signal. The Latin roots interference comes from give you a colorful picture of the meaning: entre-, “between,” and ferire, “strike.”