An arithmetic calendar is a calendar whose dates can be calculated solely by arithmetic means. In particular, it is not necessary to to make any astronomical observations or refer to any predicted astronomical observations to use such a calendar.
The Gregorian calendar including its Easter rule is arithmetic, so is the present day Hebrew calendar, but the Chinese calendar relies on (predicted) observations of the moon and sun so is not arithmetic.
Arithmetic calendars have the advantage that one can work out with certaintly which day a particular date will fall, but have the disadvantage of not being perfectly accurate. Furthermore, what accuracy they do have will perish over time owing to changes in the length of the mean solar day and other astronomical cycles.