It's a silicone rubber keypad. They're usually custom-made for the application (MOQ in the thousands or more if a mold has to be made).
They require a matching PCB that is either gold-plated or printed with a carbon paint in order to form the key patterns. The rubber keys have a conductive silicone bit molded into the back of the keys that bridges the PCB interdigitated pattern so that the switch is closed (the resistance is not nearly as low as with a switch that has metal contacts, but plenty good enough for a microcontroller to detect). The buckling of the key gives a tactile feel that is appropriate. Sealing against the environment (water, finger oils etc.) is not great, but acceptable for many applications.
Excellent choice if you're making a large quantity of a product, not so practical if you're only making a few hundred pieces or fewer.