My competitor's Alexa rank is 3,373,596 and mine is 2,155,666 - does that mean I get more traffic than them? Or does the rank rely on other factors?
I would not put much weight in Alexa ranking it can be manipulated an is not necessarily an accurate reflection of what is really happening.
In this case, it is hard to tell. When you have alex rankings in the millions, it isn't very accurate.
Alexa rankings come from data collected from computers that have the Alexa toolbar installed. Since the vast majority of internet surfers don't have a clue what Alexa is, its rankings come mainly from internet marketers and other people who work with computers a lot, so my guess (I'm NOT an expert) is that the more removed a subject is from computers and internet marketing (carving elephants from peach pits, for example) the less meaningful the Alexa numbers are for websites related to that subject.
alexa rank is determined by traffic and pageviews. if with low traffic you can get decent rank if pageviews are higher.
don't rely on alexa, simple as that they are not that good in ranking and stuff, but ya you are better than your competitor that's for sure.
Although you shouldn't rely on Alexa, a lot of people do, especially advertisers. That's why Alexa in fact is important. Alexa are using many factors to provide your stats, here's a great post about how Alexa works.