The light-gathering power of a telescope depends on the area of its objective lens or mirror. The better the resolution , the sharper the image. The larger the objective the better the resolution. Roughly - double the diameter, double the detail. Magnify - make images larger for the eye or detector.
Large magnification requires good resolution .
The magnification is given by the the focal length of the objective divided by that of the eyepiece. Telescopes split into two basic types depending on their use of a mirror or lens as an objective. Reflectors - use a mirror. Most high quality and all research grade telescopes are reflectors. Click here for an illustration of the various types of focus used in reflecting telescopes.