QUICK ANSWER
A three and out is an offensive drive that ends after three plays without a first down, usually with a punt on fourth down. It costs the offense time, field position, and rest for its defense.
A three and out is when an offense runs three plays, fails to get a first down, and has to give the ball up. It usually ends with a punt on fourth down.
A team gets four downs to gain 10 yards, but most teams only try to convert on the first three. If those plays fail, the offense usually punts or tries a field goal.
Why Three And Outs Hurt
Time Of Possession
A three and out takes very little time off the clock. Time of possession does not decide games by itself, but giving the ball back quickly gives your opponent more chances to score.
Field Position
Because the offense barely moves, it punts from close to where it started. If the other team gains some yards before punting back, your next drive may start deeper in your own territory.
That makes it harder to reach field goal range or the end zone.
Fatigue
Long drives wear down a defense. A three and out does the opposite, because the other team's defense gets a quick break.
It also sends your own defense back onto the field with very little rest. A few in a row can really hurt late in a game.
How Teams Avoid Three And Outs
The key is staying out of long-yardage situations. A sack of the quarterback or a run for a loss costs a down and yards, which makes the next play much harder.
Penalties can do the same thing. An offensive holding penalty can turn a manageable down into a long one. Once the defense knows a pass is coming, it can focus on the pass rush and coverage.
To learn more about how the game works, see this overview of football rules.