OK Wilkey, I'm going to try this. You may be disappointed because there is no real magic in a condenser lens. They are, of course, of value in some situations. I've also opted for the short (relative) explanation with one illustration.
A simple lens is one that's flat on one side and curved on the other and is thin. If you have rays of light coming from a theoretical source an infinite distance away, the rays are said to be collimated (parallel). A simple lens will take these rays and focus them to a theoretical point.

If we instead put a point of light at this focal point then the rays coming through the other side will be collimated. If there are no other optics, then this is
not called a condenser. It's called a condenser when additional optics are used. Its purpose is to provide a large area of light on something else. On a microscope it lights the stage were the slide goes. On projectors the film. On theatrical gobos the pattern or shape that's to be shown on stage. On projection headlight the shape to be thrown on the road. All of these have additional optics to focus on the stage (microscope slide) or gate (as its called in the other uses). The amount of light the lens captures depends on the focal length (where that point is from the lens) divided by its diameter. This gives the
f-number. The smaller the
f-number the more light is gathered. However, we are only getting light from one side of our point. To get more of the rest we use a reflector. A spherical one could reflect light back to the point. A parabolic one could collimate the light by itself. However in combination with our condenser lens this is not what we really want. Note however many everyday light use a parabolic reflectors either by itself or as a condenser to feed fragmented (fresnel) lens in jobs like standard headlamps. The third reflector option is the most efficient but I suspect the hardest to design. A ellipsoidal reflector with the condenser lens focused at that second focal point of the ellipse.
Now some nagging points. It turns out for many jobs the collimated beam is not the most desired. In a projection system the light should spread to cover the rearmost element of the projection lens.
Why are most condenser lens two simple lens "belly to belly"? It turns out this is not anything special about condensers. A simple lens is subject to certain problems which are called "aberrations". Putting the lens together this way (a doublet) is the simplest way to correct for these aberrations to some extent. A good quality hand magnifier would also be made this way.
What is a fresnel lens? A basic fresnel lens is one that acts like a simple lens that would be much thicker and heavier. It does this by being divided into angled segments. A fresnel does not have to simulate one large lens. Different segments could be focused in different places like a car headlight.
If we were designing a spotlight [img]/ubbthreads/images/graemlins/wink.gif[/img] and wanted sharp edges it would be designed as a projector with the edges of the gate defining our shape and size and could be adjustable (just like a gobo spotlight). If we don't need sharp edges then the projection lens and gate can go and the lens in front of the light is not called a condenser.
Did this help or make things worst?
Anyone see any errors or things that need further explaination?
edit: put in better illustration (not a simple lens though)
edit: A point I failed to mention. A mirror with the light source at its focal point produces collimated light from that side. At 2 times the focal point it is redirecting the rays back to the source. If we are using a lens then this is what we want. In reallity it needs to be just under 2 times to reduce the amount of light blocked by the very real light source.