Hi Theresa –
I think there may be two questions going on here, and I will attempt an answer as such.
The first question (and one that may not be very satisfying), is what does mm mean? This is a technical thing, referring a distance inside the camera, specifically the distance between the lens and the focal plane when the lens is focused on infinity.
The second question (and I think this is getting to heart of it), is what does the mm say about what is going to be in the field of view? The smaller the number, the wider the angle of view. On a 35mm sensor, a 14mm lens will capture 114 degrees, whereas a 500mm lens will capture a very narrow 5 degree field of view. A good illustration of this is posted at http://www.digitaltechnologyart.com/angle-of-view.html.
Once you decide what you want in your frame, your choice of focal length will have a big impact on how your image looks. Say you want a headshot, capturing your subject from the collar bone to just above the hairline. With a wide angle lens, you’d have to stand very close to your subject to get that crop. You would capture your subject and a lot of the background on either side, and your subject would be very distorted – with the parts nearest the camera, such as the nose, looking disproportionately large and those further away, such as the ears, looking quite small. Not likely a flattering shot.
Shooting with a longer focal distance, such as in the 85-135mm range, will force you to back away from the subject to achieve the desired crop (collar bone to above hairline, in this example), and in backing away, the distortion will be significantly reduced. You’ll also have a narrower angle of view, meaning less width of the background will be shown, making easier to find a non-distracting sliver of the background to include.
There’s a great tool posted at dofsimulator.net that illustrates these concepts, as well as the effect on the background blur: http://dofsimulator.net/en/.
Hope that is helpful.