Experimental studies of plasma-assisted combustion have shown that Nanosecond Repetitively Pulsed (NRP) discharges are a very efficient way to improve flame stability in lean regimes. These discharges generate a nonequilibrium plasma that induces a local heating and an important production of active species sufficient to enhance the combustion. The aim of this article is to understand the physical and chemical mechanisms involved in plasma-assisted turbulent combustion. High-performance computations of a lean bluff-body turbulent premixed methane-air flame, experimented at EM2C laboratory, are conducted for that purpose. Simulations are performed by combining a semi-empirical plasma model with an analytical combustion mechanism. Without electrical discharges, only a weak reaction zone behind the bluff body is observed. However, when the flame is assisted with the plasma, the flame power and surface increase significantly. A chemical analysis performed at the flame basis shows that the heat and the radical O produced by NRP discharges induce the dissociation of main burnt gases species H2O and CO2 into radicals OH, H, CO, O and species H2, O2. The species with long lifespan OH, H2 and O2 are convected from the center of the bluff-body recirculation zone to the flame front where they are consumed increasing the chemical reactivity. This causes a local increase of heat release rate that attaches the turbulent flame front which can develop downstream.