Welcome to the forums! Your Airstream has two electrical systems, 12v
DC and 110v AC. The 12v
system powers your fans, lights, radio, water pump, reefer (if you have that type) and anything you have plugged into your 12v
power points while the 110v system powers your microwave, air conditioner, and anything else you have plugged into your 110v household style outlets.
Your 12v system will stay charged while you're plugged in at a campground, as long as you don't engage the battery disconnect. I'm not totally familiar with the Use and Store labels. Sounds like a battery disconnect switch, though. As long as you're in the "Use" mode you should be fine. I assume the "Store" mode allows you to disconnect the battery while plugged in so you don't boil your batteries dry.
Again, welcome to the forums.