In short, a projection is used to 'flatten' the earth used for maps. 
A datum is a point of reference. 
A projection uses the datum as a point of reference, it's location on Earth. 

In GIS, there are two types of "coordinate systems": Geographic Coordinate System (latitude and longitude) and Projected Coordinate System (X and Y). 
Both geographic coordinate system's and projected coordinate systems use a datum for reference.

 - A geographic coordinate system is not projected (not flat), they are in latitude and longitude. Think of a round globe, not a flat map.

 - Projected coordinate systems on the other hand are "flat" - but still need a point of reference (datum) to define locations in space.

In other words, the datum is used to determine the point of origin on Earth by referencing a central point inside a 'model' of Earth.