What is this gray thing thing on a main water line right after it comes into house?
I can't find one that looks exactly like that, but the two most common items would be 


a check valve (one way valve) (might have an arrow molded into it)
a "constant pressure valve" (slight misnomer) - a pressure regulator with a slight, intentional leak - used to keep your pump running a long time at constant pressure (say 50 PSI) while you are using water, and then let it slowly "leak" up to 60 and shutoff, whereupon it will drop down to 40 and turn on, then rise to 50 and stay there until your water use becomes low or none and the cycle repeats.


If you watch the pressure behavior as you use water the second one should become clear, if it applies. Or it could be something I haven't met/thought of. Possibly a (disused) chlorine or other chemical injector given the fitting on the bottom? Or an air injector if you have very antique pressure tanks with no membrane/bladder.