If the pilot light will not stay lit, that is when you have stopped pushing down on the pilot light button, and then the pilot light goes out, then the issue is a faulty thermocouple. It will need to be replaced and is a more complicated procedure with special tools involved. We strongly suggest you hire a furnace technician for this work.
Now if the pilot light will not start at all, even when the pilot light button is being held down, then there is likely a problem with the gas getting to the furnace. It could be as simple as a bubble of air in the line. If this is the case and you hold down the pilot light long enough it should bleed the air bubble out. The challenge is that it’s hard to know if the issue is an air bubble. The problem could also be a damaged supply line and you will definitely want to work with a professional for this problem. If you use propane gas for your furnace, make sure the tank is not empty. If you suspect a problem with the propane tank, consult your local gas supplier.