it means that your site number 1,428,863 in popularity among people who installed alexa toolbar. or, all people that installed alexa toolbar rather visit million and a half other sites than yours.
Ok. So given this information, what can I do to improve my alexa rank over the course of 1 - 3 months? I want to try to get under 600,000.
IMHO, you are setting wrong goal. Your goals should be more uniques, less bounce rate, more pageviews per visitor. Forget about alexa, given, of course, you want to make money with your site and not just boost alexa rank.