What does it mean when your heater clicks on and the tv clicks and makes an electrical sounding noise?

Check to see wheter the heater is grounded properly.

If it is get a surge suppressor to take the "spikes" out of the system.

Many heaters use a spark ignitor which produces a d/c voltage to a ground source. This could be causing bleed over into the tv. You main ground lug on the home or in the box could be loose. OR, the 115v neutral wire (which connect to the grounding lug in the box) on the heater could be getting used as the heater ground. If so, this is definitely causing the problem.

It sounds as if you have some loose connections. Cut the breaker off for the heater and test the circuit and make sure your on the right one. Make sure the wiring is tight at the breaker and at the thermostat itself. If you live close to the ocean the salt air will corrode where the breaker attaches to the buss bar.

From your description, I believe that when your heater comes on the thermostat in the heater arcs for an instant, & generates an RF signal that is picked up by the TV.

It's not uncommon, & is not dangerous or harmfull to either the TV, or heater.

First thing you want to check when that happens is out your window. Do you see a sudden intense light shining in the windows and under the doors? If so, it won't help anything to run. Best thing to do is to quickly leave a note for your loved ones, letting them know you've been abducted.

Don't listen to everyone who's trying to freak you out.

Your heater is operating fine.

Douglas D's answer was right on the money.

It means the wiring in your house is strange and I'd be getting it checked out soon...bad wiring can lead to fires...

RUN!!!!!!