The best way to understand the double push is to watch an inline skater - the double push originated as an inline technique.
As stated in yesterday's article on Double-Push Skating and Klap Skate in Cross Country Skiing, the double push involves two pushes per leg instead of one. Instead of the normally static glide period in conventional conventional skating, "...the foot, angled on the outside wheel edge, is pulled actively inward toward the body in this phase. The pending second push is in much the same manner as with the conventional technique."
Actually, some inline skaters would have a problem with the comment "pulled actively inward toward the body in this phase". The double push is really a two pushes, not a pull and a push.
Anyways, none of this makes ANY sense until you see the double push videos of inline guru Eddy Matzger and read his comments.
(Eddy's web site, by the way, is http://skatecentral.com/. The site contains additional videos).