A nice collection of tessellation-related definitions can be found at http://www.spsu.edu/math/tile/defs/definitions.htm.
Properties of Tessellations
Symmetric/Periodic: the tessellation is self-symmetric; it's made up of a repeating motif or fundamental region.
Monohedral/Isohedral: All tiles are the same shape.
Regular: The tessellation is periodic and tiles are congruent regular polygons.
Semiregular: The tessellation is periodic and all tiles are regular polygons.
Asymmetric/Aperiodic: The tessellation does not repeat itself. Some mathematicians have discovered tiles from which it is impossible to construct a symmetric tiling!
Reptile: All tiles are the same and each tile can be decomposed into a number of smaller copies of itself.
Other: The images below show other collections of plane figures that cover the plane. Do they deserve the title "tessellation"?