Definition
Supersymmetry (SUSY) is a proposed symmetry of nature that pairs every fermion with a boson and every boson with a fermion. Each known particle would have a "superpartner" of the same mass but opposite spin statistics: the electron would have a scalar selectron, the quark a squark, the photon a fermionic photino, the gluon a gluino, and so on.
It is the only kind of symmetry that mixes spacetime symmetries with internal ones, and it is a required ingredient of all known consistent superstring theories.
Why it matters
How it works
Bosons (integer spin) and fermions (half-integer spin) behave very differently — bosons cluster, fermions exclude. In ordinary quantum field theory the two classes are independent: a symmetry can rotate one fermion into another, but not a fermion into a boson. Supersymmetry breaks that wall. A SUSY generator Q satisfies the algebra {Q, Q̄} ~ P (the momentum operator), so two SUSY transformations together give a spacetime translation.
The consequence is that every fermion field must be paired with a bosonic superpartner of the same gauge quantum numbers and the same mass — and every boson with a fermionic superpartner. The Standard Model spectrum doubles. We have not seen the partners, so SUSY, if it exists, must be broken — the partners must be heavy, with the breaking scale ideally not too far above the weak scale.
The major motivation is the hierarchy problem. Standard Model corrections to the Higgs mass involve loops of every particle, and a generic ultraviolet cutoff would push the Higgs mass to roughly the Planck scale. Cancellations between bosonic and fermionic loops in a supersymmetric theory keep the Higgs naturally light. The required cancellation works to about a factor of one part in ten thousand if the partners sit near a TeV — accessible to the LHC.
That motivation has weakened. ATLAS and CMS searches at the LHC have set lower limits on squarks and gluinos in the 1-2 TeV range, making the cancellation increasingly fine-tuned. Some natural SUSY models remain alive, especially those with light Higgsinos or compressed spectra, but the simplest "low-energy SUSY solves everything" picture is under heavy experimental pressure.