Highgate is a part of North London, up on a hill, where the houses cost a lot of money and the streets feel quiet and well looked after. People know the name most of all because of Highgate Cemetery, a large old graveyard in among the trees. Many famous people are buried there; students usually hear Karl Marx first, though actually writers and other public names lie there too. You use it as a place name: she lives in Highgate; we walked up to Highgate. The name is high + gate, and that is fair — but gate here is the old word for a road or way, not the door in a wall. So it is closer to “the high road” than “a tall door”. Always write it with a capital H; it is a place, not a kind of gate.