The Stretch Modifier changes the mesh vertices along a chosen axis (default: local z-axis) as a function of distance from the axis.
There are two different Modes: Scale and Absolute. When you switch on Absolute, the values in the Magnitude graph are the distance from the axis in units of the current project instead of a scaling factor based on the original shape of the mesh.
The Magnitude dialog allows you to define the stretch amount as an Analytic Function of position along the reference axis. You can also use a Point graph where you can generate an arbitrary function by manually placing points and setting the spline interpolation. To do this, select Point from the Function drop-down list under the graph. The example graph on the lower right shows the way it was done for the example mesh displayed below. It scales a spherical primitive mesh to a disk with a hump around a certain distance. This modifier is ideal to set up a disk with a complex structure.