Supersymmetry

As opposed to just regular "symmetry"? Remember in elementary school you were taught that symmetry means two things are alike on each side. You were given little paper cutouts and amazingly, when you folded the little starfish or monkey or whatever, it was equal on both sides and they matched.
Yeah, this is a little different:)
Supersymmetry or SUSY (in geek language) is a symmetry that relates elementary particles of one spin to other particles that differ by half a unit of spin. (Its better if you first learn what bosons and fermions are.)
For every type of boson there exists a corresponding type of Fermion with the same mass and internal quantum numbers- supposedly.
In other words, there only exists indirect evidence for supersymmetry, but it is a huge component in many theories.