Here's an example--What are you trying to do? The instructions you linked don't really mention the coin field because you don't need it if you are following those instructions ...
And to answer the question, it's the sequence results from the coin flip poketech application for a particular seed.
Frame| PID ____ | !!! |Nature|Ability| Coin _ | (...)
7904 | 4D7FF18D| !!! | Timid | 1 ___| Heads| (...)
_____________
Poketech Taps
Happiness: 657
Coin Flips: 7
_____________
What does that bolded Heads mean, there? I was guessing that when I've theoretically done 657 Happiness app double-taps and then moved to the coin flip app, the seventh coin should land Heads if I'm on the right frame for the egg to produce a shiny pokemon of a Timid nature and Ability#1.
Am I correct, or is this completely irrelevant?