Today, supersymmetry is most often talked about (at least by non-physicists) in relation to string theory, because it removes many of the theoretical and mathematical complications to the theory. In fact, the full name of string theory is actually "superstring theory" which is a shorthand for "supersymmetric string theory."
At present, we have no clear experimental evidence that conclusively proves supersymmetry is true. The most obvious evidence that physicists hope for would be the discovery of a superpartner for an existing partner.
Supersymmetry Naming ConventionsThe naming of the superpartners is a bit unusual, because the different types of superpartners have different types of prefixes and suffixes added to indicate their relation to the known particles.
If the particle is a boson, then the superpartner is named by adding a "-ino" to the end. If supersymmetry is true, then the photon (a boson) should have a related photino which is a fermion.
The fermions, however, have superpartners which are named by putting an "s-" prefix onto the term. So the electron (a fermion) has a superpartner called a selectron, which is a boson.