This is a famous quote from the first Star Wars film (technically called Episode IV: A New Hope) of the original trilogy. While the Force is mentioned several times in the film from beginning to end, the most important time that it is uttered is during the attack on the Death Star by the spirit of Obi-Wan Kenobi. The spirit of Obi-Wan said, "Use the Force Luke!"

Luke Skywalker flies his X-Wing into the trenches of the massive space station to fire a missile into a hole “that’s no bigger than a womp rat” (a very small, small opening). While there are computers on board his X-Wing to “accurately” fire the shot, an early attempt failed even using the computers. As Luke approaches the hole, he hears the spirit of Obi-Wan, his mentor, to turn off the targeting computer and let the Force guide the shot.

So as the Death Star closes in on the Rebel base, Luke Skywalker trusts his feelings and uses the Force to fire the shot heard 'round the galaxy. The shot is a direct hit, obliterating the Death Star.

More Info: en.wikipedia.org