Buoyancy is an upward force caused by the pressure from a displaced fluid. It is the force that causes wood and boats to float in water and the reason why objects feel lighter when submerged in water.

In a gravitational field, the pressure at the bottom of a fluid is higher than at the top (because of the weight of the fluid above it, as in air or water pressure). When the fluid is displaced by an object, the force from the fluid pushing up on the bottom of the object is stronger than the force from the fluid pushing down on the top of the object, so overall the fluid causes a net buoyant force pushing up. However, the object is also being pulled down by the gravitational force. Whether the object floats upward, sinks downward, or remains in a fixed position depends on which force is stronger or if the forces are equal.

The buoyant force is proportional to the volume of the fluid that is displaced by the object. The gravitational force is proportional to the mass of the object. Therefore, it is easiest to think of the buoyant force in terms of density - the density of the object (mass per volume) determines if it will float. Wood is less dense than water so it floats in water. Helium is less dense than air, so balloons filled with helium float in air. Steel is denser than water so steel objects sink in water.

How do boats made of steel float? Boats made of a metal, like steel, float because they are designed to displace a lot of water. The shape of a boat causes it to displace a larger volume of water than the metal takes up. This causes the average density of the boat (steel + empty space occupied by air) to be less than the density of the water being displaced so the buoyant force causes it to float. If the boat were filled with water instead of air, the buoyant force would be the same, but it would not be strong enough to counteract the gravitational force (the extra weight of the water) so the boat would sink. You can experiment with this concept by making a boat out of aluminum foil and seeing under what conditions it floats. What shape of boat will float? How much water can you put in the boat before it sinks? If you put the boat under water, what happens?

What happens if the object has the same density as the fluid? If an object has the same density as the fluid, then the buoyant force will be equal to the gravitational force and the object will not be pushed up or down. It will remain in whatever position in the fluid it is released from.

Here is a website that shows some examples with pictures:
pictures here

Buoyancy is a force. It arises in a system of a fluid and a solid when the solid is denser or less dense than the fluid. The buoyancy force acting on the solid (if it is denser) is the difference in density between solid and fluid times the acceleration due to gravity, 9.8 m/s^2. So, a rock dropped into a bucket of water has negative buoyancy force acting upon it.

Buoyancy is the force that is exerted by a fluid on a submerged object. The force comes about because a fluid has a pressure gradient in it the further down you go. What this means is that any kind of fluid, a liquid or a gas (in this case though it's easier to picture a liquid, like water), has some weight to it. The further down into a liquid you go, the more weight it is supporting. So at the surface of a lake, the water is only supporting the weight of all the air above it, or atmospheric pressure, about 14 pounds per square inch. As you go deeper and deeper into the lake, there is more and more water above you that needs to be supported. This compresses the water and causes it to have higher pressure. So as you go down, the pressure gets higher. When you submerge an object in some fluid, then the fluid beneath the object will have higher pressure than the fluid above the object. This causes a net force on the object acting upwards. Suppose you were to submerge a water balloon in water. The water balloon wouldn't go anywhere, because it would act in exactly the same way that the lake water would act. It has the same pressure gradients and all that. So the buoyancy force is balanced out by the weight of the water. So, for objects that weigh less, per unit of volume than water, the buoyancy force will cause the object to float. For objects that weigh more, per unit of volume (i.e: are more dense) the buoyancy force can't quite win out and the object will sink. I've attached two links where you can learn more about buoyancy and explore the concept more yourself.

Buoyancy is a consequence of being less dense than your surroundings. If everything else is denser than you are, then gravity will pull on it more strongly and it will weigh more for a certain volume. This means that you will have a tendency to rise (float) to the surface if whatever is denser than you.