These chroma sidebands are what is actually used by the color receiver to decode the color information. As previously stated, the chroma sine waves which are transmitted get compared to the local frequency/phase locked oscillator in the set, and phase deviations therefrom represent hue information. The strength of those same signals represent intensity, and this is how the complete color information is transmitted and received/decoded by your TV set.
There are some very interesting ways in which the average joe technician can see these signals in action, namely by using a vectorscope attached to the color circuits of a TV set. A vectorscope is a device which gives a visual indication of the phase angle relationship between the transmitted burst and the accompanying chroma information as decoded by the set in question.
http://en.wikipedia.org/wiki/Vectorscope
Look familiar?
It should, it's the same exact vector diagram from the I/Q video I posted earlier!
Basically the vectorscope is showing you visually the phase angle relationship of the on-screen colors (such as color bars) in relationship to the color burst, and by studying the vectorscope display you can ascertain certain things about the circuit you are attached to. Specifically if the circuit is demodulating on the correct axis (phase relationship), or if there is some phase shift which may cause the set to display incorrect colors. Most of the time these errors represent a phase shift in the demodulation circuits themselves, which usually amounts to an incorrect setting of some transformer in the color circuits. In early color receivers there is (are) normally subcarrier transformer(s) fed by the local oscillator, which shift the phase of the 3.58Mhz signal going to the demodulator tubes by a specified amount (early quadrature sets were 90 degrees, others some arbitrary amount as specified in the schematic information- so called X and Z demodulation). If this transformer is out of whack, color bars will be abnormal.
Here is a shot of the subcarrier circuit of the CTC-2, and its accompanying subcarrier transformer.
As you can see, the incoming burst is applied to a reactance tube. The function of the reactance tube is to compare the incoming burst to the phase of the local subcarrier, and 'nudge' it into phase so the signals match each other. It does this by varying the load on the crystal. This is exactly the same function as the horizontal phase discriminator (AFC) in some other sets (Admiral and Dumont notably), besides the lack of a crystal (horizontal circuits do not require the same level of stability as do color circuits). See the following schematics for similarities:
http://earlytelevision.org/pdf/Admiral_20A1_Sams_77.pdf
http://earlytelevision.org/pdf/dumon..._schematic.pdf
Vectorscopes can be bought on auction sites for very little cash, I bought a Leader unit for less than $50 recently though I have yet to try it out as my daily runner (Director 21) has some RF issues I need to sort out before I delve into the chroma circuits.