This is a theory that, at its fundamental level has supersymmetry, the posited relationship between fermions (half-integer spin, obey Pauli-exclusion principle, like quarks, electron, etc.) with bosons (integer value spin, obey Bose-Einstein statistics, like the gluon and photon, etc.), at its most fundamental level and the corresponding hypothetical particles do not have the same mass as their hypothetical superpartners. If supersymmetry were unbroken, then the particles in the hypothesized relationship would both have the same mass.
Spontaneous breaking is the most theoretically consistent idea. In spontaneous symmetry breaking, the the system itself chooses an asymmetric state while the rules itself are symmetric. An example is balancing a pencil, the rules are the symmetric, the pencil has equal right to fall left or right. But what we find is that the system, i. e., the pencil chooses a state left or right. The system has chosen asymmetry while the laws of physics remain invariant. Nothing in the fundamental equations forces a partciular choice, thus, the symmetry breaking is spontaneous.
A real world example of spontaneous symmetry breaking is the Mexican-hat shaped Higgs mechanism potential. The Higgs field's potential has many lowest energy configurations that can be settled on, giving it a potential that looks like a Mexican hat with low-energy potential outcomes at the bottom on the rim.
When supersymmetry breaking occurs, superpartner particles become much heavier whereas their masses would initially be equal to their partner particles. SUSY breaking plays an important role in Supergravity, where a modified Higgs mechanism gives rise to more massive Gravitinos.
The energy where SUSY breaking is suppose to occur is called the SUSY breaking scale, about 1000 GeV when we consider low energy supersymmetry (where the heirarchy problem is actually answered), thus, has the potential to be detected by the LHC or future particle accelerators.