I have attached all the wires into the labeled connector but I have a brown wire with an X label remaining. Does it double with another wire in one of the connections?

How did your old thermostat wire and the options of the new thermostat? All info will help.

Old thermostat was a RUUD (also the brand of my gas heater and heat pump) dial style. The old thermostat had a place for all the wires. I now have an extra brown wire labeled "X".

This new thermostat is digital opposed to the dial. My old thermostat had the option to run aux heat (heat pump) and emergency heat (no heat pump).

Once again not knowing your system and setup its hard to say. X maybe common or the circuit for aux heat.

I figured it out. The brown wire "X" is for the unit power. The Honeywell RTH6350D uses a battery for power and so this wire needs to be taped off and left open.