Why will a big reflector make more distant stars easier to see?

Unfortunately, no matter how large of a telescope you have, stars will always appear as pinpoints of light. Even the largest professional telescopes are not able to resolve stars as discs. However, if it's a dim star that one is trying to detect, it is true that a telescope with a larger diameter main objective (a mirror in the case of a reflector or a lens in the case of a refractor) will produce a brighter image of the star than one with a smaller main objective. Larger lenses and mirrors gather more light. The light-gathering ability of a telescope depends on the area of its main objective. Since the area of a circular objective varies as the radius squared (area = pi * radius^2), doubling the radius of the objective will quadruple the area of the objective, and therefore the light-gathering ability.