A batter is said to have struck out looking when he does not make at attempt at a pitch that the umpire rules a third strike. Even though he does not swing, the batter is out because the called strike is the third strike.
Batters strike out looking for a variety of reasons: surprise over the pitch that has come, belief that the pitch is outside of the strike zone or simply tensing up and not taking a swing. Official scorers mark such strikeouts with a backwards "K" to differentiate from a swinging strikeout, which is noted by a normal "K" in the scorebook. Pitchers who are having a particularly effective game will often strike out several players looking because the batters have no idea which pitch is coming and/or the pitches are veering into the strike zone from outside of the strike zone. Another way that pitchers get batters out looking is by having pinpoint control and hitting the edges of the strike zone, often called "painting the corners" or "painting the black" because some home plates have black edges.