Predictive models help you to find customers who are most likely to do something--whether that is buy your product, abandon your product, buy more of it, or buy it now.
So this is how they work. They look at your customer base and they try to find out what a certain group--let's take buyers--have in common. Typically you'd want to look at demographic information (age, gender, socioeconomic status, geography etc.), transactional information (what have they previously bought from you, how often do they purchase, how much do they spend, etc.), and sometimes, attitudinal information (are they savers, do they donate, do they want to be in control of their lives--whatever is relevant for your category).
Then, they come up with this equation that allows you to calculate a score for your customers. Now you can rank people based on their score--from who is least likely to buy to who is most likely to buy.
Models offer you two main benefits. They allow you to choose to communicate with the best prospects. Not only does this reduce your MARCOM, you are now also at less risk of annoying people with needless communications. (Hey, all I ever do is go to Alaska on your cruise lines. WHY do you keep talking to be about the Bahamas?? Do you even know me?)