While a spheroid approximates the shape of the earth, a datum defines the position of the spheroid relative to the center of the earth. A datum provides a frame of reference for measuring locations on the surface of the earth. It defines the origin and orientation of latitude and longitude lines.
Whenever you change the datum, or more correctly, the geographic coordinate system, the coordinate values of your data will change. Here are the coordinates in degrees/minutes/seconds (DMS) of a control point in Redlands, California, on the North American Datum of 1983 (NAD 1983 or NAD83):
34 01 43.77884 -117 12 57.75961
Here's the same point on the North American Datum of 1927 (NAD 1927 or NAD27):
34 01 43.72995 -117 12 54.61539
The longitude value differs by approximately 3 seconds, while the latitude value differs by about 0.05 seconds.
NAD 1983 and the World Geodetic System of 1984 (WGS 1984) are identical for most applications. Here are the coordinates for the same control point based on WGS 1984:
34 01 43.778837 -117 12 57.75961
In the last 15 years, satellite data has provided geodesists with new measurements to define the best earth-fitting spheroid, which relates coordinates to the earth's center of mass. An earth-centered, or geocentric, datum uses the earth's center of mass as the origin. The most recently developed and widely used datum is WGS 1984. It serves as the framework for locational measurement worldwide.
A local datum aligns its spheroid to closely fit the earth's surface in a particular area. A point on the surface of the spheroid is matched to a particular position on the surface of the earth. This point is known as the origin point of the datum. The coordinates of the origin point are fixed, and all other points are calculated from it.
The coordinate system origin of a local datum is not at the center of the earth. The center of the spheroid of a local datum is offset from the earth's center. NAD 1927 and the European Datum of 1950 (ED 1950) are local datums. NAD 1927 is designed to fit North America reasonably well, while ED 1950 was created for use in Europe. Because a local datum aligns its spheroid so closely to a particular area on the earth's surface, it's not suitable for use outside the area for which it was designed.