For modern elementary particle physics, The theoretical and philosophical basis is the Quantum Field Theory (QFT). In a rather informal sense, Quantum Field Theory QFT is the extension to fields, i.e. structures with an infinite number of degrees of freedom, of quantum mechanics (QM), dealing with particles.
Spin has a mathematical basis for the action of fields or particles when rotated. Particles are the quantum excitations of a field in quantum field theory, which is the basis of particle physics, and their spin represents the behavior of the field under rotations. A field that has no spatial characteristics, such as the Higgs field, is just a space-time numerical entity, and has zero spin.
Spin is an important property in a broader sense that affects the ordering of electrons and nuclei in atoms and molecules, giving it great physical significance in chemistry and physics of the solid state.