If I open up Blender v2.73 and select the cube and delete it. Then select front view ortho and add a circle mesh and check align to view. Then add a mirror modifier the mirrored part does not appear. However if I make a face (doesn't matter how, press f or extrude and edge) then the mirrored half appears. Is this a bug? I'm new to blender so don't feel confident about reporting this. This appears to work as expected in a tutorial video that I watched (Venoms Lab2 Modelling 1).
All modifiers have several options that alter the way they are displayed. Not all modifiers have every option available. The buttons for these display choices are shown at the top of each modifier -
The first two options are available to all modifiers and make the modifier visible in final render or viewport display. In object mode in the viewport with this enabled you will see the edges created by the mirror modifier.
When available the other two options effect what modifier data is shown in edit mode.
While in edit mode and with the third option disabled you will not see any of the mesh created by the modifier.
While in edit mode and the third option enabled you will see only faces drawn that are created by the modifier. This is the default for many modifiers.
The final option allows the full edit mesh to be displayed. With this enabled you can select parts of the mesh on the mirrored side. Be careful with this option as all movements are done on the real geometry only, as you select mirrored vertices and move them they will move 'backwards' to what you expect.
Also remember that with the mirror modifier, if your mesh is centred around the point of the mirror, the duplicated mesh may be located in the same place as existing mesh data.
Edges are a the equivalent of a geometrical line segment, having neither height nor width, just length. The only reason they exist is to connect the vertices, it has no visible change.
A single vertex in a similar manner is the same as a geometrical point, having no height, width, or length, just being a set of infinitesimally precis coordinates, creating no visible surface to render.
You will have to extrude the mesh in some way to make it visible at all.
Another point, made by Chebhou, is that the modifier mirrors the object based off of the origin of the mesh, if you have a complete circle mirrored on all axis, it will appear to be exactly the same. It is only when you delete some of the vertices that you notice it is actually being mirrored.