Progressives, in the simplest sense, are keeper leagues. You get to keep some or all of your players from one season, progress (thus progressive league) them to the next season, and continue the same league season after season. i.e. You might have a team made up of all guys from 1984. After you finish the season, the league starts up again, and you keep all the same players, but use their 1985 seasons. Most leagues will fill the gaps by having a draft before each season. There are all kinds of variations and ways to do it.
They're very popular, as you've heard, but I would recommend at least a few OLs first to get a feel for the game. Progressives do require some commitment.