The terminator is also the line on a planet (or moon) dividing night from day. The points at which the sun is on the horizon, just rising or just setting. Generally, the sun is far enough away from planets that the terminator can be said to divide the planet in two equal hemispheres (ignoring the equatorial bulge).
Apart from points inside the Arctic and Antarctic circles, midnight and midday are the times when you are furthest from the terminator. Dawn and dusk are when you are on the terminator. During the solstices, the North and South poles are farthest from the terminator, and during the equinoxes, the North and South poles are on the terminator.