Coincident vertices are separate, individual vertices in a single 3D object that occupy the same location in space. Essentially, the vertices are overlapping. This sort of issue can come up when combining multiple elements or along the edges of open polygons where the vertices have been snapped to one another.
Coincident vertices often cause smoothing problems when the model is rendered, and can cause errors when the model is exported to other applications. To avoid these problems, coincident vertices must be welded or attached together to form a single vertex. When you have coincident vertices, there will be times you have coincident faces as well. In some situations it may be easier to remove the coincident faces rather than the individual vertices.