In Layman's terms, spread refers to how big a diamond is when viewed table up. It is therefore a measure of diameter, length and width.
Relationship to Depth
It goes without saying that the deeper a diamond is, the less spread it will have.
On occasions, a cutter may deliberately make the diamond deeper by cutting a thicker girdle, on the diamond. This increases carat weight (and thus price), whilst having no effect of the spread of the diamond.
Therefore, since most, if not all diamonds are set table up, spread is one of the more important factors to consider, especially when considering a diamond's carat weight.
Spread of Different Shapes
Since some shapes, such as the princess cut are naturally deeper than the round brilliant cut, carat for carat, they will have less spread. Therefore, a much larger princess cut is required to match the spread of a round brilliant cut.