Prior to Chad Hedrick coming on the scene circa 1992, inline speed skaters used the same classic speed skating style as the ice speed skaters. Chad changed that with his double push technique. Now all the elite skaters use it.
The classic style of speed skating involved pushing against a fixed leg on the ice or other surface. The leg being pushed would then glide and after a distance would itself push against the other leg, now the fixed one. This cycle would repeat itself over and over.
The DP does not have this fixed leg to be pushed against. Instead this leg itself pushes toward the center line of the skater as the other skate pushes. Hence the name double push.