How big an object appears is best classified by the angle it makes when we observe it.  Let's look at some examples.  First, let's observe a wall from close up.  If we are close enough, all we can see is the wall.  The part of the wall we see takes up the entire angle of our field of vision.

Now suppose that we observe a small picture on the wall.
The small picture will also make an angle with our eye.
This smaller angle will be some fraction of the larger total angle our eye can see.

This fraction determines how big we perceive the picture to be.  For example, if our total field of vision (vertically) was 90 degrees, and the picture was 30 degrees, we could say the picture took up 1/3 of our field of vision.  Another object that only subtended an angle of 15 degrees would appear to us to be only 1/2 as big as the picture. 

To see how distance affects our determination of apparent size, hold out your thumb an arms length away.  The width of your thumb and eye make an angle of approximately 1/2 degree (interestingly enough this is the approximate angular size of the moon and sun as viewed from Earth).  Now move your thumb closer.  As you do, the angular size of your thumb becomes a larger and larger fraction of your total field of vision angle, and hence looks bigger and bigger.

What does this have to do with a telescope?  In its simplest definition, a telescope is an instrument that takes objects that appear very small (make small angles with your eye), and makes them appear large (make large angles with your eye).  Hence a telescope increases the angular size of a distant object.

Suppose we want to examine details on the moon.  Simply looking with the naked eye reveals a very tiny circle, making examination of surface detail virtually impossible.

The goal of the telescope will be to increase the angular size of the crater and the angular elevation.  In our current view, the entire moon only takes up 1/2 degree of our total vision.  It would be nice to have an instrument that would allow the moon to take up all of our vision.  This would increase our angular elevation, angular size of the crater, and allow us to spread out all the surface features on the moon over our whole field of vision.  In order to do this we need to play around with the light entering our eyes.  We need to manipulate it and force is to enter our eyes in the way described above.  To do this, we need to use refracting lenses.

When light is incident upon glass it bends.  If we shape glass in the right way, we can make a lens that will bend light in such a way that it focuses parallel beams.  Below is a picture of a refracting lens that is focusing the light from the center of the crater into a single point.

At this point, we would be able to see a real image of the moon if we put a piece of paper where the rays of light converge.  The horizontal distance it takes for roughly parallel beams (we are assuming the crater is very small and the two beams drawn are essentially parallel) to converge together is the focal length.  This focal length is also significant in the opposite direction - diverging beams of light (like you find emanating from a light bulb) can be made parallel if they originate one focal length away from a lens. (Think of the rays of light in the picture above as going backwards, toward the crater).

Now, let's add another lens:

The second lens has a short focal length, and hence dramatically bends the incoming lights from the first lens.  The resulting rays emerge roughly parallel (if we were looking at the exact center of the crater, they would be exactly parallel).  Notice two very important things:

1. The rays from the crater on the top of the moon are now entering our eyes from below - hence the moon will appear upside-down.

2. The angle of elevation (or declination, now that the moon is flipped) of the crater has dramatically increased.  Let's examine this change more closely:

Let's examine the part of the moon between the crater and the center.  To the right in the diagram above we can see that the original angle of elevation spanned this region.  Because this was such a small angle, it was impossible to see details in this region (remember - very small angular size implies very small apparent size).  With the aid of the telescope, the angle of elevation has increased tremendously - perhaps almost to the entire lower half of our field of vision.  This means that the region that used to be only a fraction of a degree in the sky (a fraction of a thumb's width at arm's length) now takes up almost half our entire field of vision!!  Now we can examine all the rich detail between the crater and the center of the moon.

A very powerful telescope might allow the following.  Instead of aiming at the center of the moon, now aim at the center of the crater.  The angle of elevation will now be defined as the angle spanning the region from the center of the crater to the top of the crater.  With the naked eye, this tiny angle may be so small that the crater itself is not visible at all!!  But with the right configuration of lenses (particularly a second lens with a VERY SMALL focal length - to bend the light very dramatically), we can make the angle of elevation span half our field of vision.  Applying symmetry to the other half of our field of vision, the crater will now span our entire field of vision.  Now we can investigate details in the interior of the crater!

Wait a minute, why can't we make a telescope capable of looking at atoms on the moon using the same argument?  Technically we can, but the main problems are:

1.  Making precise enough optics so the light beams do exactly what we want them to do (there are engineering as well as absolute, immutable limitations on this).

2.  Remembering we only have a finite amount of light to work with.  Looking just at a tiny crater (as described above) with a tiny telescope would be like painting an entire house with a teaspoon of paint.  The amount of light entering our telescope is related to how big our first lens is.  Granted it is a LOT BIGGER than our pupil, it still gathers only a finite amount of light.  If we keep on magnifying, the intensity of light goes down and down (a little like zooming in on a digital picture until you see individual pixels, or trying to light up all of Madison Square Garden with a single candle).

But with precisely ground and reasonably sized lenses, we certainly can do quite a bit of magnifying and retain clarity and reasonable brightness.