An orbit's Apsis is either its closest point to the object being orbited (Periapsis or Periapse) or the furthest point (Apoapsis or Apapsis or Apoapse), for orbits with some Eccentricity. The terms Pericenter and Apocenter similarly mean the closest and furthest points in the orbit from the center of mass.
The Argument of Periapsis (or Argument of Perifocus or Argument of Pericenter) is an angle describing where the Periapsis is in relation to a reference plane. For example, if a Comet's orbit is inclined to the Ecliptic (the solar system's plane), then the Argument of Periapsis is the angle through the plane of the comet's orbit from its intersection with the Ecliptic to the direction of the comet's Periapsis.
Specific terms are used for bodies orbiting the Earth or Sun, which are sometimes used loosely for other bodies: