More specifically conditā is the ablative singular feminine of conditus meaning "having been built" so ab urbe conditā more literally means "from the city having been built".
Also don't get it confused with ab urbe condītā which means "from the city having been made savory"
when we add m like urbem does it mean a city or the city?
Either of them.
urbem is the accusative case, but since Latin had no articles, it could be "the city" or "a city".
And what about the regular one with s urbes?
urbs is nominative singular (the city, a city); urbes is nominative plural or accusative plural (the cities, some cities, cities).