The Buoyant Force is the net force on an object by the surrounding liquid. Also, when an object is put in a liquid, the object displaces fluid equal to the volume of the object. Now it is possible to understand the Archimedes Principle.
Archimedes Principle, paraphrased: The buoyant force on an object is equal to the weight of the displaced fluid.
This all assumes there is gravitational acceleration due to a net force acting on the system.