A vector scope is used in the repair of TVs. A normal CRO can only show you instantaneous voltage/vs time or voltage/vs voltage, whereas a vector scope can do some funky "demodulation" for you and can show you phasors... so, it should be able to break down baseband composite video so you can monitor it's different components: luminance, chroma, sound (L+R)/2, sound R/2, colourburst..
That left hand image with all the compressed sine waves at differnt levels looks like it is showing you at least part of a single line of TV - the colour burst on the "back porch", followed by part of a vertical white bar (white is the lowest signal level in TV, since TV pictures are inherently "not black", white has the lowest level so that less transmission power is used on average) then the staggered steps there would be your "active line" information - obviously it's showing a test pattern that consists of some vertical bars, perhaps it is that test pattern in the third picture there, which actually has a vertical white bar as the first colour.
Actually if you count the number of steps on the left image after colour burst, there are 7, and there are 7 colour bars on the right hand test image.. I hope my exam tomorrow goes well ;-)
I've not actually used a vector scope but I'm pretty sure it's along those lines :-)
- Paul
[Edit - looks like the documentation for this suggests that was also used to monitor the baseband video signal for day to day broadcasting at transmitter stations/studios - I guess that makes sense, it would be the "dials and guages" for the engineers/operators maintaining the transmitter equipment. Vector scopes would also be invaluable for evaluating the performance of and debugging new television prototypes, I guess...
Actually vector scopes wouldn't have to be TV specific, it would be handy to have phasor relationships on screen for other radio-related things as well.]