Why does light refract when it passes through two different mediums having different densities?

You can consider first Huygens Principle of light propagation that tells us that light propagates through secondary wavelets produced by every point on a front of a light wave.
This seems complicated but I'll try to show it with a diagram:

This is a kind of mathematical construction where you have that each point on a front (for example, you can imagine the fronts as the crests of your wave) will produce small spherical waves whose envelope will give you the next front.
When the wave meets a different medium (different density) the speed of the wave in this new medium will change and so the secondary wavelets will change in size producing a "deformation" in the next front!!!!!!

The dark blue spherical secondary wavelets are smaller than the original ones, so, together, their envelope will produce a slightly bent front representing a new direction of propagation of the wave.

The easy explanation can be observed through an example:
imagine a platoon of soldiers marching on a parade ground: they are perfectly trained and you can imagine them marching in perfect unison; now imagine that they meet a different surface, a sandy beach kind of surface, at a certain angle.
The first soldier of the first row entering the sand will decrease his speed then the second as well, the third as well. etc.
Each one will slow down in reaching the sand and in doing so will change his direction and the direction of the entire platoon!

Hope I didn't confuse you even more...!