Optical telescopes are the most common form of telescopes. They work by magnifying visible light, so they are the simplest form of telescope; we can see optical light ourselves, so there is no need to use an electronic detector to process the light recieved by these telescopes.
Optical telescopes are the oldest form of telescope; they have been around since the time of Newton and Gallileo, and even before then. They have been in use for centuries; most of our knowledge about the sky comes from data gathered with them. Aristotle, for example, used observations of stars to try to detect stellar parallax; he did not detect it, and so determined that the universe is geocentric. Later astronomers discovered that stellar parallax does exist, although it is barely perceptible; much of the data used to demonstrate this came from optical telescopes as well.
Optical telescopes have several benefits over other kinds of telescopes. First, most stellar objects that give off any form of radiation give off at least some quantity of visible light, so optical telescopes can be used to detect many different stellar objects. Also, visible light has a very short wavelength as compared to radio waves, microwaves, and even infrared light, and the resolution of a telescope increases with a smaller wavelength, so optical telescopes can attain a higher resolution than can telescopes based on each of those kinds of light. With radio waves, another commonly observed form of radiation, the difference is such that a reasonably small optical telescope can get a resolution similar to that of a massive radio wave collector.
A typical Newtonian reflecting optical telescope works by reflecting light with a convex mirror onto another mirror which is at an angle in order to reflect the light into the eye piece.
A typical refrator telescope workds by refracting the light through a convex lense, then through a half concave lense, and then has it focus in the eyepiece.
The Hubble Space Telescope is the main optical telescope we have orbiting the Earth. Even though it is not the biggest telescope it can get better resolution than telescopes on Earth. This is because the Earth's atmosphere reflects and distorts some of the light coming to the Earth. The Hubble Space Telescope is not effected by this reflection and distortion because it is outside the atmosphere, thus it can get better resolution than telescopes on Earth.
Here are some pictures the Hubble Space Telescope took.
The planet Saturn
A spiral galaxy
Optical telescopes are not used for any specialized form of astronomy; rather, they are used in part for all kinds. Because most stellar objects, and especially most large stellar objects, like stars, emit visible light, optical telescopes can be used to detect many things that an astronomer would want to look for. Because of its relatively high resolution, it is easier to make precise measurements of stellar objects as well. Many stellar objects do not emit radiation far above the frequencies of visible light, so going with higher frequencies makes it hard to view all but the brightest, most energetic objects; in any case, Earth's atmosphere absorbs most high-frequency radiation. Also, because optical telescopes are relatively simple and small, and inexpensive, as compared with other forms of telescopes, they are very popular with ameteur astronomers.
Astronomers would need to use telescopes that operate in other regions of the electromagnetic spectrum for specific purposes. For example, an astronomer might look for radio waves in order to measure objects that are emitting very little energy, such as black holes. Looking at the precise wavelengths of light that are given off by an object can show the chemical composition of the object, but some wavelengths that are useful for this purpose are not in the visible spectrum. Telescopes have been created that can detect light in several of these spectrums, and they are very useful because they can be used to gather more information about objects, but they are also far more complex and expensive than single-spectrum telscopes; they are less common and harder to get, so they are not used as often. There are many reasons to use telescopes that measure light in all areas of the electromagnetic spectrum, but it is generally best to start off with optical telescopes.