I just checked the Wikipedia about this (so it may or may not be that reliable, but I'll check a couple of other sites later).
This is that it said:
I think that students who were serious about Divination would have taken Arithmancy - although it is a little weird that Hermione loved Arithmancy while hated Divination... oh well, heheh.
The name Arithmancy is derived from two Greek words – arithmos (meaning number) and manteia (meaning divination). Arithmancy is thus the study of divination through numbers.
I also checked the HPL, and this is what it had on the subject:
I believe that this subject also has something to do with names and the numbers associated with them. For example, according to this editorial on Mugglenet, Harry is a number 5, which is the number of instability. I think that this could show that this could be used as something like astrology or the chinese zoological calender.
Arithmancy is a branch of magic that is concerned with the magical properties of numbers; someone who practices Arithmancy is called an Arithmancer. For example, in the 1200s, Bridget Wenlock, a famous Arithmancer, discovered the magical properties of the number seven. An O.W.L. in Arithmancy is required to apply for a curse-breaker's job at Gringotts'.
Arithmancy at Hogwarts is taught by Professor Vector. In her class, students are expected to write essays and to be able to understand complicated number charts, which are part of their homework. Hermione Granger appears to be the only Gryffindor in her year who attempted an O.W.L. in this subject (which is her favourite).
I think that this is a Roman or Greek version of the calanders above - I wouldn't put complete trust in the art, it's inprecice and (like the editorial mentions) you'd find better canon evidence to characters in the books.