What is Snell´s Law?

How does refractive indices change the angle light moves through a medium.

The speed of light changes depending of the media the light is traveling through.
Thus, placing two different medias next to each other forms a boundary layer where the two materials touch. 

The light bends at this junction when it travels through the two materials in accordance to Snell´s Law named after Willebrord Snellius, stating the following:

n1 sin θ1 = n2 sin θ2

where n1 and n2 are the refractive indices of the two medias,  θ1 and θ2 are the angle of incidence.

This optical phenomena is broadly used across most applications within optical instrumentation as this is one of the fundamental principals on light and material interaction.

An example from everyday life is for instance when a straw is placed in a glass of water and it appears to bend at the water-air interface.