What will I do with the wires that are connected with the mercury in the old thermostat

What do you want to do, change thermostat?
Identify all wires before disconnecting anything

What will I do with the wires that are connected with the mercury from the old thermostat since I will replace it with a new digital thermostat

You will need to Identify the wires before removing the old, reconnect the New, program and turn Air Handler back on, It would be good to turn off the Air Handler while replacing. A Local recycler should take the old Mercury thermostat.

Particularly Look for terminals marked Red, White, Blue, Yellow , and Green.
May have more or less and may be different colors.