Physicists can explain a lot of things that happen in the universe, like existence of energy, the bending of space-time etc by using a handful of particles and forces. The standard model predicted that everything in the universe should be massless, but we know that’s not true. So Physicists such as Peter Higgs and Tom Kibble came up with the Higgs mechanism responsible for the generation of massive particles. And in 2012 the Large Hadron Collider found the Higgs Boson which proved the existence of the Higgs field and validated the Higgs Mechanism.
Although we can explain a lot of things with the Standard Model but it is still incomplete. SuSy is an extension of the standard model which aims at explaining some of the phenomenon which is left unexplained by the standard model, just like the Higgs mechanism.
If you take a spherical ball and rotate it in any possible way, the end result is still the same. The sphere is said to be symmetric under rotation. Similarly, if an equation remains the same if we transpose force terms with matter terms or vice versa, the equation is said to be supersymmetric.
It turns out if the universe has this property a lot of problems which we face in the standard model are elegantly solved. Three of the most important problems solved by SuSy are-
SuSy predicts that for every fundamental particle that exists there exists a supersymmetric cousin called a Sparticle which has a higher mass than the particle itself.
The interactions between the Higgs boson and other standard model particles predict that the Higgs Boson should be a very heavy particle contrary to what we found at the Large Hadron Collider.
Physicists have long wanted to unify the forces of nature into one fundamental force which describes all the phenomena that takes place in the universe. Ever since humans existed we saw the moon moving across the sky and objects falling down to earth when thrown in the air.
Isaac Newton unified these two phenomena into the one force of Gravity. Similarly James Clark Maxwell unified Electricity and Magnetism into Electromagnetism by showing that the two forces are just different consequences of the same basic principles.
The Strong and Weak nuclear interactions along with Electromagnetism have different strengths at all energies.
However if SuSy is true then the three forces converge at a single point rather elegantly. A theory that unites the forces mathematically is called a Grand Unified Theory, a dream of physicists including Einstein. Therefore even though there has been no experimental evidence for SuSy, there are more than ten thousand scientific papers written about it.
SuSy not only has application in the micro world of particle physics but it provides a solution to one of the biggest problems in cosmology. Astronomers have known for a long time that the galaxies are spinning much faster than they should spin given the amount of mass that they contain. So to save astronomy and solve this problem, Dark matter was hypothesized.
Neutralino, the supersymmetric cousin of the neutrino is the most likely candidate.
Therefore, if SuSy is true it will solve problems both of the quantum and the cosmic scales. The Large Hadron Collider at Cern is in its Second run and one of the things its is looking for is the existence of supersymmetric particles.