3. Datum

 From the Geodetic Glossary:

datum - (1) Any quantity or set of such quantities that may serve as a referent or basis for calculation of other quantities. In particular, a geodetic datum, chart datum, or tidal datum. The plural form is datums.

A datum is a measurement reference surface. Absolute positions are either from a datum or a mathematical surface related to a datum.

There can be regional or global datums; assumed or rigorously defined. In plane surveying when we assume the Earth is flat over small areas, our datum is a flat plane. Once we cover larger parts of the Earth, our datums become more complicated.

Geodetic Glossary:

datum, geodetic - (1) A set of constants specifying the coordinate system used for geodetic control, i.e., for calculating coordinates of points on the Earth....
(2) The datum, as defined in (1), together with the coordinate system and the set of all points and lines whose coordinates, lengths, and directions have been determined by measurement or calculation.

A datum is more than just a surface. It includes the collection of measurements, marks, and computations which are made with respect to the datum's mathematical surface. A physical bench mark is part of a vertical datum - when you use it you are automatically connected to that datum. 

There are many types of datums depending on the type of measurement or desired result. Surveyors are familiar with and routinely use Horizontal and Vertical datums, so those are the two we will cover.