Show ID numbers is there to tell you the correct formation or unit number (as it is known in Mobhack) to you without having to go into Mobhack.
The formation number is shown in the formation part of the buy screen and then when you go into the formation buy, the ID numbers for each prospetive unit is shown alongside that one.
I thought it was shown (the unit database ID number anyway) in the encyclopaedia, but apparently not -
that would be a useful addition.
It can be useful for end user error reporting, rather than having him learn mobhack if he is not so inclined.
I find it useful in the German OOB - I look up the sort of formation I want using the database search utility in mobhack (search for formations of class inf-at) - find the formation ID number, and then swap back to the game and scroll through the infantry looking for (say) formation 41 rather than trying to pick out an Infantrgswverttrpenfart or whatever composite mouthful of German is the formation name
!
The Formation ID numbers you are probably getting confused with are the formation ID letters (GH02 etc). That is on by default for users of the full game, and I usually never turn it off as it's extremely handy. I think the F3 key toggles that one.