An Edge is a line segment between two 3D positions. The most important aspect of Edges is that when referenced their end points do not need to match across photographs. What is being marked and referenced is the edge or line on an object and not the end points of that line or edge.
An Edge is a "first-class" object like Object Points are. That means Edges are computed by Global Optimization and affect Global Optimization results. In PhotoModeler only Object Points and Edges are used in Global Optimization.
One typically uses Lines (which connect Object Points) when there are well defined points in the photo and which can be matched across photographs. When there is a "line" or "edge" in a photograph that does not share distinct end points with other photographs (or they are not visible in other photographs) then Edges are more appropriate.
See also Edge Defining/Modifying.