It is roughly proportional to the square of the aperture size. A telescope with an aperture twice the diameter collects approximately 4 times as much light.

The more light a telescope can gather (and focus into your eye, onto a photographic plate, or onto a CCD), the dimmer the objects it can resolve, and the brighter it can make those dim deep sky objects appear.

A telescope with an aperture of 8 inches gathers approximately 40,000 times as much light as the naked eye.