The periodicity (set under Mesh (tab) => Global Parameters) is to ensure that your mesh on one side matches the mesh on the other side... Once you see the DEZ (data entry zone), you will understand what you need to fill in. Periodicity is set on the geometry so that the generated mesh comes out periodic, so if you go back to set it, you must regenerate.

Even if you are copying your mesh around to create an annulus instead of a periodic section, it will be easier if you have nodes matching.

Once you copy the periodic mesh into place, you can merge the sections together by using "Edit Mesh (tab) => Merge Nodes (with a tolerance)". I usually set the tolerance very close to zero and use the "single edges only" option. Don't forget to "ignore projections".

However, you could just interactively merge nodes (especially if you don't have a periodic mesh), however, you may also need to use split edge and move nodes... Still, even the manual method without periodicity shouldn't take too long for this example