As I understand it, there are several definitions of common, but I can't find any source that can highlight the etymology of the phrase.
The linked definitions are pretty rigorous, but a less strict, collapsed version might boil down to two relevant definitions:
- Common, as in shared amongst many in the group (a common goal)
- Common, as in general, appearing frequently; widespread (a common sight)
- "4c : just satisfying accustomed criteria : elementary " (The third definition is cited directly from M-W at coleopterist's suggestion)