You can subdivide a polygon face into triangles or quadrangles. Divisions are added either exponentially or linearly. To understand the difference, see Smooth Options.
To divide a face
Exponentially subdivides the face or edge recursively. The Linearly setting subdivides the face into an absolute number of segments. In addition, with the Linearly setting, you can specify subdivisions in U and V.
You cannot use the Add Divisions feature on faces that contain holes. Also, you cannot subdivide concave faces unless the center point is inside the face.
To subdivide a concave face into convex parts, use the Multi-Cut Tool or Mesh > Triangulate. To remove holes use Triangulate.