The foot valve goes at the "foot" of the piping in your well/cistern/lake, etc. It acts as a one-way valve to prevent water from draining out of the pipe when the pump isn't running.
This is correct. Keep in mind that a "check valve" is a "one way valve" that keeps the water from returning to the source. The main difference in the "check" and the "foot" valve is the location. A "foot valve" is technically a "check valve" that is located at the bottom of the well drop pipe - thus the name "foot".
A check valve can be installed near the pump since it is mostly a safety device. A "foot" valve is installed on the "bottom" of the drop pipe.
Since a check valve will also stop the water from going back down the well, you might wonder why you need the foot valve.
The main reason for the foot valve being at the bottom of the well is to maintain a drop pipe that is filled with water. The weight of the water in the pipe will help keep the valve closed when the pump is off and keeps the pipe full. This way, when the pump turns on, the water in the pipe helps keep the pump from losing it's prime while starting a flow of water.
If you only have a check valve at the top, it is true that the water in the storage tank won't drain back down the well, but gravity will leach the water from the drop pipe. When the pump turns on, there may not be enough water in the pipe to maintain the prime while the pump pulls a fresh flow. Even if it does prime, you will most likely send a pipe full of air into your storage tank. A few starts like that and you will replace the water in the tank with only air.
If you have no check or foot valve, there will be no water available for the pump to prime itself.