Curve Distribute Between Vertices

Default Options

With the default options, "Curve Distribute Between Vertices" will distribute vertices forming an edge path between your selected vertices along a (dynamically created and not retained) NURBS curve passing between the vertices you've selected:

Note: The vertices selected adhere to the same logic as Select Edges Between Vertices.

Proportional Distribution

The default distribution type for this tool is "Uniform", however you can select "Proportional" distribution in order to retain the same relative spacing between the redistributed vertices:

Use Selection Order

If your selected vertices form a path with multiple directional changes, you'll want to check the "Use Selection Order" option for the most predictable results:

Close the Loop

If you want the curve along which your vertices are distributed to form a closed loop, you must have selected "Use Selection Order", and "Close":

Create a Deformer

If you check "Create Deformer", locators will be created for manipulating a wire deformer connected to your mesh: