Anamorphic lenses are additional optics for home projectors that can take stretch an image wider than the native resolution of the projector would suggest. In the early days of projection (digital or CRT), this meant a 4:3 image could be made wide. These days it means making a 16x9 image into a wider-than-wide 2.35:1.
The idea is a lens is mounted in front of a projector, and it is either manually or automatically slid in place during movies of 2.35:1 or wider aspect. The projector or other video processor vertically stretches the image, so everyone appears tall and skinny. The anamorphic lens then stretches this image wide, making everyone appear correct, and creating a wider image in the process.
The advantage is being able to use the entire digital chip (DLP, LCD, or LCOS) for increased brightness on 2.35:1 native movies. The downside is potentially lower contrast ratio because of the additional lens elements.
Film cameras and cinema projectors also use anamorphic lenses for much the same purpose.