What kind of heating system is this for?
It should be Red is power and White is the return back to system to trigger the heat on and off.
If you use the regular Nest you will need to run a new cable to have a C wire.
The Learning Nest is supposed to work without a C wire.
OK go to the furnace and take the front cover off.
Find the thermostat wires and take picture of all the screws in a row showing the labels on the screws.
We need to see if this is a standard heating system and if there is a C common terminal.
Is it a natural gas heating system?
Can you go to the system and show us a picture of the thermostat wiring connected to the system?
The regular Nest non learning version needs 3 wires to work and looks like you only have 2 wires coming out of the wall.