textured filling circle

If you just want the texture to show, you just need to unwrap the mesh. However, this will leave you with a square texture mapped to a ring, and it wont "follow the path" so to speak.

To do this, things are only a little more complicated. First, unwrap your mesh (select all > U > unwrap). Then go to the UV editing tab.

Select the two vertices at the top of one of the edges that is on the side (because it's side edge is perfectly vertical). Press S + Y + 0. This will make the two points at equal "height" on the y axis. Do this for both the top and bottom edges, so you're left with a rectangular shaped quad.

Then, select the whole mesh, making sure the quad you created is the active face (lighter color). If you need to make it active, just un-select and re-select the face - just make sure all the faces are selected when you're done. With your mouse over the 3D view port (not the UV map), press U and select Follow Active Quads. Confirm in the box that pops up and your UV map will be straightened.

From there, just scale the UV island back to size and place it where you want in a the UV space. Add a texture and you're done.