Turbulent magnetic reconnection is believed to occur in astrophysical plasmas, and it has been suggested to be a trigger of solar flares. It often occurs in long stretched and fragmented current sheets. Recent observations by the Parker Solar Probe, the Solar Dynamics Observatory and in situ satellite missions agree with signatures expected from turbulent reconnection. However, the underlying mechanisms, including how magnetic energy stored in the Sun's magnetic field is dissipated, remain unclear. Here we demonstrate turbulent magnetic reconnection in laser-generated plasmas created when irradiating solid targets. Turbulence is generated by strongly driven magnetic reconnection, which fragments the current sheet, and we also observe the formation of multiple magnetic islands and flux-tubes. Our findings reproduce key features of solar flare observations. Supported by kinetic simulations, we reveal the mechanism underlying the electron acceleration in turbulent magnetic reconnection, which is dominated by the parallel electric field, whereas the betatron mechanism plays a cooling role and Fermi acceleration is negligible. As the conditions in our laboratory experiments are scalable to those of astrophysical plasmas, our results are applicable to the study of solar flares. Laboratory experiments reveal the underlying mechanism of turbulent reconnection, including electron acceleration. These findings are directly relevant for studies of flares in the solar corona.