The LCD below is from a cheap digital clock which was (obviously) damaged (broken glass).
The electrical connection between the PCB and the display was realized with this pink strip.
...and consists of alternating rows of conductive and insulating material between the pink boarders.
[above image was altered in contrast/brightness to highlight the alternating strips]
What is this kind of connector called? Is it only used for displays?
I am pretty impressed that the connection is reliable just from the very slight pressure between the strip and the PCB. Also, its easily removable from the display. There seems to be some conductive layer on the glass, from where the signal goes into the displays internals. This connection seems to be damaged for the three rightmost signals, where the glass is broken.