Aperture is the single number that decides how faint you can go. This estimates the faintest star your telescope can reveal under good dark skies and how many times more light it gathers than your naked eye. Because light grasp rises with the square of aperture, a 130mm scope gathers nearly 70% more light than a 100mm one, which is a bigger jump than the numbers suggest.
Limiting magnitude is on the astronomical scale where bigger numbers mean fainter: the dimmest stars the naked eye sees from a dark site are about magnitude 6, while a 200mm telescope reaches past magnitude 13. The figure here is the theoretical reach in good conditions. Real-world results depend on sky darkness, how dark-adapted your eyes are, the object's altitude, and atmospheric steadiness, so treat it as the ceiling rather than a promise.