Photo Stream lives in iCloud, and is there for any device that is signed on with the same iCloud account to access.
If you are seeing a Photo Stream on your Apple TV, then it is coming from an Apple device (iPhone, iPad).
When you sign a device onto iCloud, turn the Photo Stream option to ON, and then take pictures with that device, they go to the Photo Stream.
When you see a Photo Stream on your Apple TV, if it is not coming from one of your devices, but from another device with a different iCloud sign on, then the person's whose device they are from can share it with your devices by creating a shared photo stream.
Do you know the origin of the Photo Stream you are seeing on your Apple TV?