Incoming links means links from another website to yours. Also referred to as inbound links. Your summary was correct. However, the links need to be on sites that the AJ spider crawls, so the more "visible" the site is linking to you, the better.
PFI = pay for inclusion which means you pay a flat fee to get them to list your site quickly, though it doesn't guarantee you anything as far as ranking is concerned. And, as Warren said, AJ will only be doing PFI for a little under two more months.