An officina is basically a workshop of a mint. They would be under separate management, and so required to put their ID mark on a coin so that the manager could be hunted down if he was removing the trace amount of silver (about 5%) from the bronze coins for personal gain.
Officina numbers would be alphabetic in order, e.g.
1=A=Alpha
2=B=Beta
3=C=Gamma
Latin speaking areas would use Latin letters, and Greek speaking provinces would use Greek letters.
Collectors like to know it, but it very rarely makes any difference in price.
In (roughly) descending order of value, regardless of true rarity:
1. Rare emperor, usurper, or wife
2. Rare reverse type
3. Rare bust type
4. Rare mint for the type
5. Rare officina for the mint and type.
The sheer number of varieties in late bronzes preclude any real efforts to "collect everything", thus even varieties in the R4-R5 range (less than a dozen known) will rarely fetch more than $20 if it's for a common emperor, type, and mint.