the number on all tubes is the size in CENTIMETERS. so A68xxxxxx is 68 centimeters or 26.7717 inches (27 rounded) A63xxxxxx is 63 centimeters, which is 25 inches...etc.
inductance is the measurement of a coils resonance. a wire wrapped around an iron core will resonate at a particular fashion. this is measured in HENRYS (or for smaller values millihenries.) it's definition is technically... The induced electromotive force of one volt produced when the current is varied at the rate of one ampere per second.
wrapping a coil of wire around a nail, powering it, and using it to pick up paperclips is a very simple example of inductance. you can also wrap another length of wire around that nail and measure a small voltage being produced when you connect and disconnect the battery even though the 2 coils are seperate. This is how transformers work.
the yoke coil on the tube is "tuned" to a particular frequency that must coincide with the signal put into it. if the signal isn't right, (and it doesn't take much to be off) like i mentioned before, you end up with all kinds of geometry issues. horizontal width issues, Vertical size issues...etc. etc. etc. the difference of a few milihenries is enough to cause all sorts of issues.
we are talking about a stream of particles PERFECTLY timed, flying along at 480,000 inches per second... which is 27,272 miles per hour... to time this signal perfectly to line up perfectly at the beginning of the line scan each time a line is scanned (to have a nice straight square picture) takes some SERIOUS timing.