Exchange bias in core-shell nanoparticles has been an area of intense research. While several research efforts have been devoted in understanding the role of interfacial spins in the nanoparticles that exhibit exchange bias, a clear understanding of the spin dynamics of the core and the shell remains to be investigated. A detailed study has been carried out on the magnetic properties of Fe/γ-Fe2O3 core-shell structured nanoparticles synthesized by thermal decomposition method.Our  focus is to understand the spin dynamics of the core and shell independently and their role in triggering exchange bias (EB) phenomenon. The nanoparticles exhibit memory effect and aging associated with a superspin glass state (SSG). We show that the energy barrier distribution shows two maxima that marks the freezing temperatures of the core and shell. Lastly, hysteresis measurements after field cooling reveal a strong EB indicated by a loop shift. The onset of EB is at 35 K when the ferromagnetic core is frozen and the moments in the ferrimagnetic shell begin to block resulting in enhanced exchange coupling.