Why does we observe that when stick is kept in water then it appears to be bend under water?

The light as we know needs a medium for its propagation. Every medium has its own refractive index which is usually taken with respect to air. For sake of simplicity the refractive index of air is taken as unity.

When we see any object, the light from that object travels through medium of air and reaches to our retina. The light has its specific wavelength and speed during its propagation.

When an object is placed such that it is in two medium, the light travels from both the media before reaching our eye.

Here the two media are air and water. Water has higher refractive index than air which causes refraction. Due to the change in medium the speed of light decreases. The refraction causes difference in speed of light the stick kept in water appears to be bent or broken.