In its simplest form, it involves constantly pressuring puck carriers in the O zone and neutral zone, instead of coasting to block passing lanes like many other teams do. They're trying to force turnovers or rush them into less accurate passes that can stunt a team's transition game.
This, and their preferred off the rush style when they're healthy and on their game, require a ton of skating.
So not only do you have to be a good skater to fit in Bednar's system well, you have to be in great condition. I think the condition aspect is why we've seen guys like Comeau and Calvert take a year to find their game with the Avs.
I also think all the skating and potential fatigue are a factor in why they have so many injuries.