These are often found in pocket calculators, DECT phones, and other devices with a simple monochrome 7-segment or low-resolution display. They are used to connect the conductive tracks on the glass of an LCD to a set of pads on a circuit board below. (These displays sometimes suffer from dead segments or rows of pixels.)
Screws or twisted metal tabs commonly secure a metal frame, which compresses the elastomeric strip between the LCD and the circuit board. Release these to separate the LCD and the elastomeric strip.
The elastomeric strip consists of conductive and non-conductive layers which alternate along its length. There are several for every connection to the LCD, eliminating the need for precise alignment.