So, without a hardware clock (like the DS1307), you will be a few seconds per day off (potentially), and your internal clock will reset every time power is tripped.
While, with a hardware clock, you get more accurate timekeeping, plus the time will be correct if power is tripped.
That is correct, but although the crystal in a hardware clock could be a little more accurate than the arduino crystal, it can still drift a second per day.