Yeah, it's a black box method. Would it help to reflect on what it means, practically?
Suppose you have a black box with two BNCs. What is it?
Plug it into a VNA. This applies RF to one port (i.e., hooked up a 50 ohm amplifier, which transmits at a variable frequency), and measures the power transmitted (to the other port) and reflected (back to the amplifier; a carefully balanced network separates the transmitted and reflected waves).
The various frameworks (h, Y, s, ABCD...) are just different ways of expressing the same thing, usually with a purpose in mind. h-parameters are easier to measure at low frequencies, s-parameters at high. Matrix decomposition methods tease apart the different parameters of the system, so they can be more easily worked with (but, this probably doesn't interest you much, because math).
Maybe this is way ahead of where you're at (what's a VNA?). Suppose you just probe the box with a multimeter. Suppose it's a resistor network! How can you tell what it is? It could be some
complicated mess, but all that can be reduced to a few resistors. (To be exact: (N^2 - N) / 2 resistors, for N nodes.) For the two-port box, if you connect the grounds together, it has N = 3, so needs 3 resistors.
You have 3 unknowns, so you need to collect at least as many parameters. Note that resistance is a ratio of voltage to current, so you need four parameters (e.g., two voltages and two currents), but only end up with three in the end (one gets eliminated).
That's easy to see, because to measure a resistance, you have to apply
some voltage (or current), but the exact amount doesn't matter, as long as it's nonzero: it's a free variable.
So, you might apply a voltage between nodes 1 and 2, and measure the resulting current flow, and measure the voltage on nodes 2 and 3. You now have V12, I12 and V23. Lastly, you can short nodes 2-3 and measure the current, to get I23. Now you have a complete set of data.
Alternately, you could apply voltage to nodes 2-3 and measure voltage V12, to obtain 3 voltages and 1 current. You can't measure only voltages, or only currents, because then you can't find the resistance.
The symmetries at work here, are very similar to those of geometry: you can define a triangle from three sides, or two sides and an angle, or one side and two angles; but not three angles, because then there's no length reference. Learning how the underlying symmetries work, can save you from a lot of trouble manipulating equations you're not otherwise very prepared to work with (like because your eyes glaze over every time you look at it!) -- anywhere you see the wrong combination of numbers being multiplied and divided together, or different amounts being added or subtracted, you can be sure you've made a mistake.
Tim