Any location on Earth is described by two numbers--its latitude and its longitude. If a pilot or a ship's captain wants to specify position on a map, these are the "coordinates" they would use.
Actually, these are two angles, measured in degrees, "minutes of arc" and "seconds of arc." These are denoted by the symbols ( °, ', " ) e.g. 35° 43' 9" means an angle of 35 degrees, 43 minutes and 9 seconds (do not confuse this with the notation (', ") for feet and inches!). A degree contains 60 minutes of arc and a minute contains 60 seconds of arc--and you may omit the words "of arc" where the context makes it absolutely clear that these are not units of time.

Calculations often represent angles by small letters of the Greek alphabet, and that way latitude will be represented by λ (lambda, Greek L), and longitude by φ (phi, Greek F). Here is how they are defined.

Latitude

The latitude angle lambda

Imagine the Earth was a transparent sphere (actually the shape is slightly oval; because of the Earth's rotation, its equator bulges out a little). Through the transparent Earth (drawing) we can see its equatorial plane, and its middle the point is O, the center of the Earth.
To specify the latitude of some point P on the surface, draw the radius OP to that point. Then the elevation angle of that point above the equator is its latitude λ--northern latitude if north of the equator, southern (or negative) latitude if south of it.

[How can one define the angle between a line and a plane, you may well ask? After all, angles are usually measured between two lines!
Good question. We must use the angle which completes it to 90 degrees, the one between the given line and one perpendicular to the plane. Here that would be the angle (90°-λ) between OP and the Earth's axis, known as the co-latitude of P.]
 

Lines of latitude

On a globe of the Earth, lines of latitude are circles of different size. The longest is the equator, whose latitude is zero, while at the poles--at latitudes 90° north and 90° south (or -90°) the circles shrink to a point.

Longitude
On the globe, lines of constant longitude ("meridians") extend from pole to pole, like the segment boundaries on a peeled orange.


Every meridian must cross the equator. Since the equator is a circle, we can divide it--like any circle--into 360 degrees, and the longitude φ of a point is then the marked value of that division where its meridian meets the equator.

 

Longitude lines or "meridians"

What that value is depends of course on where we begin to count--on where zero longitude is. For historical reasons, the meridian passing the old Royal Astronomical Observatory in Greenwich, England, is the one chosen as zero longitude. Located at the eastern edge of London, the British capital, the observatory is now a public museum and a brass band stretching across its yard marks the "prime meridian." Tourists often get photographed as they straddle it--one foot in the eastern hemisphere of the Earth, the other in the western hemisphere. In the medieval times Ujjain was designated as zero longitude for Indian calculations of astronomical tables. Kanchipuram and Kurukshetra also served similarly

A lines of longitude is also called a meridian, derived from the Latin, from meri, a variation of "medius" which denotes "middle", and diem, meaning "day." The word once meant "noon", and times of the day before noon were known as "ante meridian", while times after it were "post meridian." Today's abbreviations a.m. and p.m. come from these terms, and the Sun at noon was said to be "passing meridian". All points on the same line of longitude experienced noon (and any other hour) at the same time and were therefore said to be on the same "meridian line", which became "meridian" for short.

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Adapted from Dr. Stern's "From stargazers to Starships"