Please bear with me Im a new owner and know nothing electrical. I'll try to offer up as much info as possible! :-)

My washer and dryer are on a gfi I think (with the black and red buttons and a tiny light on it) I also had a small pool filter plugged in there as well. I came home to a tripped breaker (says wash/dry/furnace) I thought it was overloading it because of the filter. The dryer , filter and the a/c were off (Its central air so its not on the plug). At first the breaker wouldn't go back to on position. After a while it would but the light isn't on the outlet anymore and the a/c won't turn on either.

Any ideas?

The Dryer is usually 240 volts, but if 120 volts, and a GFI, (when a GFI is working correctly), you will be able to trip and reset it, if not you may not have power going in, or not hooked up correctly, Line goes to line side, White to white screw, and hot to darker screw. If it trips, remove Load side, I problem is gone now, then the Load may have a fault to ground.
Washers and Dryers Usually have their own receptacle and are NOT GFI Protected.

Washers and Dryers Usually have their own receptacle and are NOT GFI Protected.

True, however I suspect that the dryer is a gas dryer and would be plugged into a 120 outlet (GFI protected).

If the breaker is a regular breaker, not a GFI breaker, resetting it should restore power to the outlet. The GFI outlet may also be tripped due to a ground fault. Unplug everything from the outlet and press the reset on the outlet.

If the breaker is a regular breaker (not GFI) and it was tripped, you are correct that it tripped due to overload. It is unusual to have furnace and wash/dryer on the same circuit. Of course labeling could be incorrect.

The fan motor in the furnace would be in use in conjunction with the air conditioning system.