It can also be used to describe a yarn color "Aran" or "Aran white"...which is just cuz the Aran sweaters are generally knit in a simple natural white or untreated/natural wool. It's one of those terms that can be used to describe just about anything involved in the knitting process.
Most worsted and heavy-worsted weight yarns will look quite nice in an Aran pattern, and of course you don't have to stick to the white color. Keep in mind though that Aran knitting has lots of cables and stitch patterns--so solid colors work best (and probably nothing too dark, don't want all that hard work to get lost!)
Good luck! I looove a good Irish-knit sweater. Itchy--but purrrdy.