What John refers to must only be an American thing. I remember watching the Sopranos before, and they referred to tomato sauce as gravy, which I thought was really strange. In the UK gravy only refers the type of sauce that Joe talked about, made from the juices of the meat. Nowadays you can buy granules in a jar to make the sauce, which people often use instead.

Mum and experienced cook here. In standard English 'gravy' is a sauce made from meat juices. You take the juices from roasting the meat, add seasoning, and adjust the consistency to make it suitable for pouring. This is what is meant when someone says 'mashed potatoes with gravy'. It's also possible to buy granules, cubes and so on to make instant gravy. There are variations in which other ingredients are added, such as 'onion gravy' and 'mushroom gravy', but the basic meat-juice sauce is still the same. The meaning is slightly different in the cuisine of the southern states of the USA. Here, 'gravy' is a thick creamy sauce, often containing pieces of meat. However, this is not what most English-speakers outside this region would understand by the term.

If I add to mashed potatoes meat with its sauce (roast meat), can I call it "mashed potatoes with gravy"?

Gravy is a specific type of sauce like tomato sauce or soy sauce. It's specifying which kind of sauce you like with your potatoes.

Gravy is sauce made from the natural juices created when cooking meat. Generally, mashed potatoes are eaten with beef or turkey gravy in the USA. Hope this helps :)