This is because of an optical effect called refraction, where a pencil seems to be bent when put into water. 

Light bends as it moves from one optically dense medium to another; this phenomenon is called refraction. 

Transition is from air to water in this context and as a denser medium it results into bending of light.

The speed of light is higher in air compared to water hence when light enters water, it slows down since the two mediums do not mix uniformly. 

The change in speed results in light diverting or changing its direction.

 This bending occurs according to Snell’s Law which involves the refractive indices of the two media and the angles of incidence. 

Your brain will assume the light rays are straight when you see a pencil partially placed under water. The rays of light coming from the submerged tip of a pencil bend when they leave the water towards air. This makes submerged tip seem to be in an off-centered location. The resultant effect appears as if the pencil is broken or bent in a funny way at the edge of the water body.