Just like the white noise you hear in the background of audio files (that annoying hiss, hum, whistle, buzz, etc.), digital photography "noise" is the random imperfections, graininess, or rough texture you sometimes see in photographs. The two primary types of photographic noise are color noise (colored specks or splotches) and luminance noise (grainy imperfections).
To reduce noise in photography, always make sure to expose your images correctly in-camera and take pictures at the lowest possible ISO. To reduce noise in your photographs in post-production, you can use a third-party app like PhotoDirector.