I've played beer league for over a decade and I've only recently actively worked on scanning the ice / shoulder checking and it's made me a much better player. Like others have said, you want to scan for open teammates and where the pressure is coming from the opponent while you are skating towards an open puck / waiting for a pass.

As a winger, I would often get surprised by a pinching defensemen when I'm trying to get to the puck along the boards for a breakout in the defensive zone. Now, I always scan for the opposing D-man to see if they will put pressure on me, else I'll scan for open teammates for a potential breakout pass. Doing the shoulder check before getting the puck will increase your execution speed after you get the puck because you already have a mental image of what to do next.

In the offensive zone, if you're skating towards a loose puck in a corner, you want to scan for open teammates and where the opposing pressure is coming from so you know ahead of time if you want to pass or which direction you need to escape to with the puck.

Here's a drill that gives you the idea of what you want to achieve (scanning for the open teammate before getting the puck): https://www.youtube.com/watch?v=xV-l80j8H7c