Any object, totally or partially immersed in a fluid or liquid, is buoyed up by a force equal to the weight of the fluid displaced by the object.

Archimedes' principle allows the buoyancy of any floating object partially or fully immersed in a fluid to be calculated. The downward force on the object is simply its weight. The upward, or buoyant, force on the object is that stated by Archimedes' principle above. Thus, the net force on the object is the difference between the magnitudes of the buoyant force and its weight. If this net force is positive, the object rises; if negative, the object sinks; and if zero, the object is neutrally buoyant—that is, it remains in place without either rising or sinking. In simple words, Archimedes' principle states that, when a body is partially or completely immersed in a fluid, it experiences an apparent loss in weight that is equal to the weight of the fluid displaced by the immersed part of the body(s).

Consider a cuboid immersed in a fluid, its top and bottom faces orthogonal to the direction of gravity (assumed constant across the cube's stretch). The fluid will exert a normal force on each face, but only the normal forces on top and bottom will contribute to buoyancy. The pressure difference between the bottom and the top face is directly proportional to the height (difference in depth of submersion). Multiplying the pressure difference by the area of a face gives a net force on the cuboid ⁠ ⁠—  the buoyancy ⁠ ⁠—  equaling in size the weight of the fluid displaced by the cuboid. By summing up sufficiently many arbitrarily small cuboids this reasoning may be extended to irregular shapes, and so, whatever the shape of the submerged body, the buoyant force is equal to the weight of the displaced fluid.

 weight of displaced fluid = weight of object in vacuum − weight of object in fluid

The weight of the displaced fluid is directly proportional to the volume of the displaced fluid (if the surrounding fluid is of uniform density). The weight of the object in the fluid is reduced, because of the force acting on it, which is called upthrust. In simple terms, the principle states that the buoyant force on an object is equal to the weight of the fluid displaced by the object, or the density of the fluid multiplied by the submerged volume times the gravity.
Based on the text below, how would you explain Archimedes’ principle to a 10 years old child, using the example of an object immersed in water?
When you immerse an object under water, it pushes the water away in order to take its place.
The water wants to get back to where it was before and pushes the object away, towards the surface.
Then it depends what is the weight of the object, compared with how much water was moved.
Imagine you could put your object on one side of a balance, and on the other side, you would duplicate your object and transform it into water (representing how much water is moved if you were to plunge put your object under water).
If your original object is lighter than its equivalent in water, like a bubble for example, or a balloon, the water will be strong enough to have the object to float.
If the object is heavier than its equivalent water, like a bowling ball, or a rock, the water will not be able to push hard enough, and the object will sink.