As you probably know, in general, 3D elements may be listed from worst to best in the following order: tetrahedrons < wedges < hexahedral. Wedge elements (also known as prisms or pentahedrons) combine the advantages as well as disadvantages of tet and hex elements. They are often used together with hexahedrons when geometry is too complicated to fill it with hex elements only. They are better than tets so such mix is more preferable than hex+tet. They can also be used for transition between tetrahedral and hexahedral elements.
Wedge elements also have some special applications. They can be used to mesh solid models that are axisymmetric (not to be confused with actual axisymmetric approximation often used in FEM). They are also very useful for boundary layer mesh in CFD as well as for some simulations in fracture mechanics.
