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The radio, the antenna cable and the antenna collectively make up a system.

The radio has an impedance - a complicated cousin of resistance. In theory, 50 ohms

The cable has an impedance. Nominally 50 ohms at RF frequencies.

The antenna has an impedance. By design - 50 ohms

In reality manufacturing tolerances accumulate, things don't work quite as expected, et cetera. there are differing impedances. mismatches.

a portion of the incident wave - the wave generated by the radio and sent out the cable - bounces back at an impedance mismatch.

this reflected energy collides with the incident energy and does three things:

distorts the ougoing signal
reduces the signal leaving the antenna
heats up the output transistors

1 to 1 ratio down the line - 50 ohms, radio, cable and antenna - would give you 1:1 SWR

2 to 1 ratio of reflected to incident is destructive; 3 to 1 sends up little smoke signals of surrender from the finals

http://www.youtube.com/watch?v=yCZ1zFPvrIc&feature=related

http://www.youtube.com/watch?v=ic73oZoqr70&feature=related

3D physical standing wave
http://www.youtube.com/watch?v=NpEevfOU4Z8&feature=related

tutorial
http://www.youtube.com/watch?v=w1eE13UXAKs