This is the original CDTV remote control by Commodore, second version. The Commodore part number is 252594-02. The difference to the first version is that the switch between mouse and joystick is a sliding switch instead of rubber buttons.
While this remote is perfectly usable for it's original purpose - controlling the Amiga CDTV - it's probably even more popular purpose is controlling the Chameleon, thus serving as a wireless game controller.
Thanks to it's 40kHz transmission standard, the CDTV remote control has outstanding reach and it is remarkably insensitive to the direction that you're pointing the remote to: Even if you point the remote to a white wall at the opposite of the room, the Chameleon will safely catch the buttons that you're pressing. A direct line of sight to the receiver does help, but it's not always required: There is no need to point the remote control exactly into the direction of the Chameleon, like you may know it from TV remote controls.
Please note that if you are ordering a Chameleon, the CTDV remote control is already included in that price. Batteries are not included. You will need two AA cells to operate this remote control.