The first question that comes up is, "How do we define an orbit?". To answer this, we will look at an Earth, or geocentric orbit.
However, the same concepts can be applied to an orbit around any mass.

For the purpose of this explanation, we will use simplified orbital mechanics, assuming that the orbiting body is perfectly spherical, and that the mass of the orbiting object is negligible compared to the mass of the parent.

To define an orbit, we have a set of what is called orbital parameters:

Apogee
    The highest point in the orbit. For calculations, we will use R_a, the distance from the center of the Earth to the orbiting object at apogee.

Perigee
    The lowest point in the orbit. For calculations, we will use R_p, the distance from the center of the Earth to the orbiting object at perigee.

Inclination
    The angle of the orbit as it crosses the reference plane, in this case, the equator of the Earth. For instance, a 0 degree orbit is a East-bound orbit directly around the equator.

Eccentricity
    The measure of how "close" an orbit is to being circular. More covered in the next section, Orbital Calculations

Period
    The time it takes for the orbiting object to complete one orbit.

Semi-major Axis(SM_a)