What is buoyancy?

Buoyancy is the upward force acting on an object.

For example if you see cork floating on water. Now why does cork floats on water?

It floats on water because the density of cork is less than the density of water.Because the density of cork is less than the upward force the cork floats on water.

In this video bubbles are filled with methane gas. The bubbles float up because of buoyancy. Lighting them on fire is just a bonue! ;-)

Similarly a nail sinks in water because the density of nail is more than the density of water. Because the upward force is less than the density of nail the nail sinks.

This video shows a classic experiment, the Cartesian diver, when the depth of the diver depends on the buoyant force acting on it. Changing the density of the diver (by changing pressure) will change the buoyant force. video from: Noel Pauller