Aperture (the diameter of the lens or mirror) is the single most important factor determining the performance of a telescope. The larger the aperture, the more light your scope gathers and the higher resolution (ability to see fine detail) it has.
The clear aperture of a telescope is the diameter of the objective lens or primary mirror, specified in either inches or millimeters. Doubling the aperture means doubling resolution and quadrupling light gathering power. This means that an 8-inch scope can see things that are only one-fourth as bright as the limit of a 4-inch scope and details that are only half as big as the best that the smaller scope can resolve.
Larger scopes also have longer focal lengths, meaning greater magnifications and image sizes are possible with both the eye and cameras.
Greater detail and image clarity will be apparent as aperture increases. For example, a globular star cluster such as M13 is nearly unresolved through a 4" aperture telescope at 150 power but with an 8" aperture telescope at the same power, the star cluster is 16 times more brilliant, stars are separated into distinct points and the cluster itself is resolved to the core.
Photos of Saturn demonstrate what increasing aperture will give you -- higher contrast, better resolution and a brighter image. Top to bottom with Celestron telescopes: C5 (5" aperture), C8 (8" aperture) and C14 (14" aperture). All were taken using eyepiece projection photography at a focal ratio of f/90. The effects of aperture are even more pronounced during visual observation.