When you cut a logo out of thick acrylic, then push that through the metal face of a sign with the same logo cut out of it, you have a push-through sign. Add lights behind that combination and voila, you've created a push-through illuminated sign.
Seriously though, push-through signs are an excellent way to combine a variety of materials to create a very high-end effect with the illuminated edges of acrylic that extend beyond the metal face of the sign. .