What does it mean when a laptop on sale is a store demo model?

Store demos are the ones that have been on the display counter for whoever wants to play with the buttons can do so ; refurbished would be better, and be sure that if you buy the demo, you get a complete warranty

That means that the one you are seeing is the store demo one. The one intended for people to look at in the store all day long.

With the demo mode you can't set passwords

First off 'refurbished' does not mean bad condition. Refurbish is just a product that is not 'brand new' and is cleaned, fixed (if any issues), and repackaged by the company and sold for a lower price. But to answer your question 'store demo model' is the laptop that you see laying out in the stores when you walk in. It's the actual laptop that people see, touch, and use in the store to see if they like it. So it's safe to assume that it's been used and might have some wear/tear on it.

It's the one that's been sitting on the shelf for everyone to look at.

I would not expect it to have been heavily used and it should not be damaged, though minor scuffs or scratches would be no great surprise. You will want to check how it affects your rights. The battery life will probably be shortened a little, since laptop batteries degrade over months and years of use.