The second down indicates that one play has previously been run by the offense and a first down was not achieved. The 1 is the yardage remaining in order to reach a first down. In most cases this means the offense has just run a play on first down which resulted in a nine yard gain.
The nine yards gained can also be a combination of a five yard penalty and a four yard gain.
The offense has the advantage in an early down short distance situation. They could just pick up the one yard by running up the middle, maybe with a quarterback sneak. An offense can also use the down as a chance to take a shot down the field to try and gain a big chunk of yards. They would do so knowing that they would have a third down and one, even if they threw an incompletion.
The best case scenario for a defense when faced with second and short is to tackle the offense for a loss resulting in third down and a medium yard distance. That can happen with pressure, which is called a blitz. Blitzes are a good way to sack the quarterback or tackle the running back for a loss.