This software is useful for understanding how localized electronic interactions affect electronic bands. Namely, how the fact that electrons feel localized and strong electronic repulsions when located in the atomic orbitals of the same atom changes their behavior away from what single-electron band theory would predict. For example, if electron-electron repulsions on the localized 3d orbitals of a transition metal cation are so strong that having two electrons on the same cation would create a prohibitive cost, then the electrons on those cations would prefer to localize in order to avoid moving around and finding themselves on a cation with another electron. This is the Mott mechanism for insulating behavior, something that one-electron-at-a-time theory can not describe correctly. Other (less dramatic) effects due to localized electronic interactions include magnetism or the energetic narrowing of electronic bands.
This software is a post processor: one does a first-principles calculation, typically within Density Functional Theory or DFT (which is a type of band theory that is one-electron-at-a-time), obtains some electronic states, and then begins to wonder how the electronic properties may change due to localized electronic interactions. One then needs to create an orthonormal localized orbital basis (Wannier or Lowdin functions, for example) and compute the one-electron Hamiltonian in that basis (i.e., a tight-binding representation) and output that information to a file. Then the BoSS software can read that tight-binding data, add interactions on top of that, and (approximately) solve the interacting electron problem in that localized basis. Specifically, BoSS solves an extended Hubbard model representing the electronic system. The "subsidiary-boson" method is one of a large number of approximate many-body approaches to solving complex interacting electron problems.
Please note that theories such as DFT+U or hybrid functionals are actually not fully interacting electron theories and thus do not actually describe electronic correlations via the effect of a "Hubbard U" or non-local exchange-like integrals. Those approaches are still within the broad category of "band theory": independent electrons that feel a self-consistent one-electron local or non-local potential. They can, in principle, give correct total energies for an interacting system but the description of the quantum state and excitation spectra are fundamentally over simplified by construction and do not include correlations (multiple Slater determinants or configurations).
To use this software, you must be able to (i) run a band structure calculation of some variety (DFT, DFT+U, hybrid, Hartree-Fock, etc.), (ii) create a tight-binding representation the electronic bands of interest (e.g., via Wannierization or computation of Hamiltonian matrix elements between localized orthonormal functions such as Lowin orbitals), and (iii) be able to convert that information into a format legible by the BoSS code which natively reads the data format output by the Wannier90 software.