The limiting magnitude is the apparent magnitude of the faintest object that is visible with the naked-eye or a telescope. The limiting magnitude of a telescope depends on the size of the aperture and the duration of the exposure. Generally, the longer the exposure, the fainter the limiting magnitude.
After dark adaption and under the very best observing conditions, the limiting magnitude of the human eye is about magnitude 6.5. However, this is an average, and some people have reported seeing objects fainter than this. At night, from a busy city with lots of light pollution, the limiting magnitude may drop to magnitude 1 or 2, meaning that only the brightest stars are visible.
Astronomical surveys will often set a magnitude limit and attempt to detect all sources brighter than that magnitude. For surveys of very distant objects, such as galaxies or quasars, this introduces a bias where only the brightest of the more distant objects are seen (known as Malmquist bias). Very distant objects with 'normal' or 'low' brightnesses are not detected because they are fainter than the limiting magnitude of the observation.