Yes the Apple TV device will work with any TV that has an HDMI Port.
If your TV has an HDMI port then the Apple TV device will hook up to the TV and work with any TV that has that HDMI port.
If your TV is an older TV that doesn't have an HDMI port then it will not work with that TV but as long as you have an HDMI port on your TV which the newer TV's do then the Apple TV box or device will work with your TV.
A HDMI cable hooks into the TV and then into the APPLE TV device.