1. (sometimes capital) new, recent, or a new or modern form or development: neoclassicism; neocolonialism. 2. (Geological Science) (usually capital) the most recent subdivision of a geological period: Neogene. [from Greek neos new]. Also, esp. before a vowel, ne-.
Although optical telescopes are the type most commonly used for stargazing and amateur astronomy, lots of astronomical research is done on telescopes that look at other wavelengths of light. Each of these wavelength ranges shows us something unique about the universe and allows us to view events and objects that can't be seen with human eyes.
How far can I see with a telescope? Pretty far. Usually this question is asked when comparing two scopes, as in can I see farther with this telescope?. A bigger scope will show you more, but not necessarily farther. You don't really need to see farther, though. With the unaided eye, you can see 2.8 million light-years to the Andromeda Galaxy. Even a very small telescope can show you an object called 3C273, a quasar in Virgo that is 3 billion light-years distant. But most objects that are interesting to look at aren't that far away. What you really want with a telescope is light-gathering power to see fainter things, not farther things.