The Minimal Supersymmetric Standard Model (MSSM) is an extension of the Standard Model of particle physics that incorporates the principles of supersymmetry (SUSY). Supersymmetry is a theoretical symmetry between fermions (particles with half-integer spin, like electrons and neutrinos) and bosons (particles with integer spin, like photons and W/Z bosons). The MSSM proposes a partner particle for each particle in the Standard Model, effectively doubling the number of particles.
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The Minimal supersymmetric Standard Model is the supersymmetric extension of the Standard Model with two Higgs doublets and the minimal superpartner field content needed for a renormalizable theory.