The focal length is the distance from the front of the lens to the imaging surface (i.e., film or digital sensor). Focal length is measured in millimeters (I have never seen it measured any other way). The focal length determines, among other things, the angle of view. This angle determines how much stuff fits into the frame (yeah, I said stuff).
The Math
The shorter the focal length the wider the angle of view. The longer the focal length the narrower the field of view.
Practically speaking what does this mean? If I want to photograph a whole building while standing close to the building I need a short focal length (wide angle of view). If I stay in the same spot and try and take a picture of the same building using a long focal length (narrow angle of view) I will only be able to capture a small portion of the building.
With the rise of the digital single-lens reflex camera (DSLR) the concepts of focal length and angle of view have become a little more tedious. Most consumer DSLR have a sensor size smaller than a piece of 35mm film so depending on the lens and camera combination the true focal length may be different than the focal length printed on the lens. There is something called a crop factor. I think I'll save that for another time.
Here is a interesting resource that demonstrates the concept of angel of view very nicely.
Here is a resource that better explains focal length and angle of view
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