Twilight:

Informally, the period of time when there is light in the sky before sunrise, or after sunset.

The 3 calculations of twilight are:

Civil Twilight

Civil twilight is defined when the sun is 6 degrees below the horizon. This is the limit at which twilight illumination is sufficient, under good weather conditions, for terrestrial objects to be clearly distinguished; at the beginning of morning civil twilight, or end of evening civil twilight, the horizon is clearly defined and the brightest stars are visible under good atmospheric conditions in the absence of moonlight or other illumination. In the morning before the beginning of civil twilight and in the evening after the end of civil twilight, artificial illumination is normally required to carry on ordinary outdoor activities.

Nautical Twilight

Nautical twilight is defined when the sun is 12 degrees below the horizon. At the beginning or end of nautical twilight, under good atmospheric conditions and in the absence of other illumination, general outlines of ground objects may be distinguishable, but detailed outdoor operations are not possible, and the horizon is indistinct.

Astronomical Twilight

Astronomical twilight is defined when the sun is 18 degrees below the horizon. Before the beginning of astronomical twilight in the morning and after the end of astronomical twilight in the evening the sun does not contribute to sky illumination; for a considerable interval after the beginning of morning twilight and before the end of evening twilight, sky illumination is so faint that it is practically imperceptible.

What's an Azimuth?

You probably already know the definitions for sunrise, sunset, moonrise, moonset, moon phase, and a number of other terms used by the tools described in the article in the left-hand column. But there's a few you may need some extra help understanding:

Altitude:

 In the context of celestial calculations, the distance, expressed as an angle, at which a body appears above the horizon.

Azimuth:

The point at which a vertical line from a heavenly body intersects the horizon. Note that in astronomical measurements, the arc is measured from the South point, while in navigational measurements, it is from the North point. Make sure you know which one your tool is showing you.

Dawn Line:

 A curved line applied to a map that shows the relative position of first light at any given time.
Those clocks that show a world map of where the sun is currently up have moving dawn (and dusk) lines on them.

Transit Time:

The time at which a heavenly body crosses the meridian (mid-point in the sky) of a given location.