What is Higgs field and why Light has no Mass? 

Higgs Field is the reason why particles have different masses.

It is basically a theoretical field that exists in every region of our universe. Higgs field gives mass to fundamental particles like Quarks and Leptons which make up the ordinary matter. The interaction of other particles with this field decides their mass. That is, the more they interact with higgs field, the more massive they will be.

Light is made up of Photons and photons do not interact with Higgs field that is why light appears to be mass less.

To get your head around this idea, think of Higgs field as an ocean. The water represents Higgs field and water molecules represent Higgs Bosons which are basically small bits of Higgs field.

Now imagine a small fish moving swiftly in the water, by interacting less with the water the fish can move fast and hence has got less Mass.

At the same time, a chubby fellow can only move very slowly in the water because his body interacts more with water and hence he has got more mass. This is just an analogy, in fact, we only hear about Higgs Bosons and these particles are basically bits of higgs field..

Higgs Bosons are also known as "God Particle". Scientists at CERN using Large Hadron Collider discovered Higgs Bosons back in 2012 and prediction of Peter Higgs proved to be right..