Slow motion is when time appears to pass more slowly, as if a recording is being played back at reduced speed. This can be used as a visual effect or as part of the gameplay.
Slow motion is usually used as a visual effect in cutscenes. For example, when something really awesome is happening on screen like a fight. Adding slow motion lets you see every little detail and contemplate the coolness. In these situations, slow motion is used when somebody closely dodges something to show how close the character was to getting their face blown off, or to show off a large explosion in the background. Using slow motion at the right time is key. If it feels out of place, the cinematic will feel corny and cheap. Us it at the right time and it may get a "wow" out of the player.
Slow motion can be used as part of the gameplay. In some games, slow motion is a way for the player to get out of tricky situations. For example, in Need for Speed: Most Wanted, by triggering slow motion, the player can make really tight turns and drive through roadblocks. In other games, when using slow motion your enemies are in slow motion while you are not, letting you lay waste to your foes (as in Bayonetta and Dead Space). You may also find yourself walking around in slow motion after an explosion almost hits you, or when you're hit by a flash grenade. Slow motion is usually a power up or a reward for playing well. Sometimes, in action games, slow motion is described as some kind of "focus" that the character uses to be really badass.