Here's the basic explanation I used for a few friends of mine who didn't know what was going on.

...I am far from an expert, so if I screw any of this up someone smarter is welcome to correct me.

All matter is made up of Atoms; which are themselves made up of Protons, Neutrons, and Electrons. Protons and Neutrons are also made up of something called Quarks. Electrons are not composed of anything smaller and are a member of a group called Leptons.

So at the very smallest level we have Quarks, and Leptons; however, there is also something else called Bosons. These Boson particles are responsible for the fundamental forces that allow Quarks and Leptons to interact with each other. These forces are: Electromagnetic, weak nuclear, strong nuclear, mass, and maybe gravity. The Higgs boson is the particle responsible for mass; it is heavier than the other particles and interacts with a special field called the Higgs field in a unique way.

The Higgs field is an invisible force (similar to a magnetic field) that affects all particles. Lighter ones such as Photons pass through it easily, but heavier ones like the Higgs boson face resistance and sort of drag the field with them (think of it like ripples on the surface of a pond.) This interaction between the Boson and the field is responsible for giving matter its mass.

Now the discovery of this particle is important because up until now its existence was only theorized, but it was required to confirm our model of fundamental particles (all the stuff I just explained.) It is basically the last hole we needed to fill in our periodic table of realities make-up.

The Higgs was hard to discover because of its high energy (125 GeV) and the fact that it only exists for a small fraction of time before decaying into lighter Photon particles. The LHC (Large Hadron Collider) was built for the very specific purpose of finding this specific particle; it cost 7 billion dollars and took around 30 years to get it up and operational. It has finally served its primary purpose.

So that's basically it in a nutshell; the discovery of the so-called "God particle."

Now you know, and knowing is half the battle.