I know it's a bit confusing... that's why I documented in the wiki after I got it myself
The key point is that both mappings (main and alt) are active at the same time,
and that it's possible for a mapping to only be partial (i.e. only define what extra buttons you want).
It's also only useful if your controller has more buttons than what is required by the core.
If say your controller is a simple SNES and you use all your buttons for the core (6 + start/select + dpad), then you can't use any alternatives.
So let's look at some more examples:
Amiga core with 2 buttons, games use "up" to jump
For this, it's convenient assign a third physical button (b3) to "up", so you can use both up and b3 to jump.
(you can just skip the rest of the buttons)
for this the alt mapping is empty except for "up"=b3
NES core with 2 buttons, adding "turbo"/autofire
Assign A and B to two extra physical buttons (b3 and b4).
After the mapping is done, activate the autofire feature by holding b3 or b4 then press the OSD button (while OSD is closed).
This results in having A and B as regular buttons as b1 and b2, but then b3 and b4 act as turbo/autofire for the same button.
for this the alt mapping has b3=A and b4=B
"Slowdown" function
Some old physical controllers for NES and PCE such as the NES Advantage have a slow-mo function that works by using an turbo/autofire function to Start. Just map an extra button to start (say b5, a shoulder button away from face buttons) and set it to turbo as described above.
This makes the game pause/unpause continously, making it go slower than normal.
as above, the alt mapping only needs to have b5=Start
Neo Geo combo buttons
For this you need to make a physical button overlap two core buttons. It's not possible with only one map.
It's also not possible to reuse the same physical button in the same map, so you need to split assignment to your "combo" button across 2 maps.
For example for A+B: main: b1=A, b3[combo]=B / alt: b3[combo]=A, b2=B
It helps to write it down on paper to work out how to make more buttons, but hopefully the example above with 3 combo buttons is enough for most cases.