Consequences of having too low tyre pressure
As others have answered already, the most common problem with low pressure is pinch flats
I think with thick and inflexible sidewalls it can also damage the sidewalls of a tire over time. However if you have flexible, lightweight tires (e.g. cyclocross/gravel or performance oriented MTB tires) this shouldn’t be a problem.
At very low pressures the tire can “roll off” the rim in tight turns.
I think I’ve written this on StackExchange several times, but my favorite method for gauging minimal tire pressure is to put the front wheel on a sharp corner (e.g. edge of a curb or stair) and push down on the handlebars with your whole body weight. If you can press it down all the way to the rim the pressure is probably too low, unless you ride very carefully.
Of course low pressure increases rolling resistance, but with good, performance oriented tires the increase is surprisingly low.
The Schwalbe Smart Sam is a pretty good and supple tire. 40 psi (2.8bar) is low for a 37mm tire but can still be fine with a lightweight rider (how light are we talking here? 50kg? 60kg?) and bike. But you should be careful when riding over potholes, roots, tram tracks etc.
As a 65kg person I went as low as 2bar on 33mm tires in cyclocross.