A stick standing in a half-filled bucket of water appears bent because of the refraction of light. When light passes from one medium (air) to another medium (water) with a different density, the path of the light is bent, which is known as refraction. This bending of light causes the apparent position of the stick to be shifted from its actual position.
In the case of the stick in the water, the light waves from the part of the stick below the water's surface bend as they pass from the water into the air, causing the light waves to change direction. This change in direction makes the part of the stick below the water appear to be at a different position than it actually is. Our brain interprets this as a bend in the stick, but it is actually just an optical illusion caused by the refraction of light.