Flare events are mainly due to magnetic reconnection and thus are indicative of stellar activity. The Kepler Space Observatory records numerous stellar activities with unprecedented high photometric precision in flux measurements. It is perfectly suitable for carrying out a statistical study of flares. Here we present 540 M dwarfs with flare events discovered using Kepler long-cadence data. The normalized flare energy, as defined by the ratio to bolometric stellar luminosity, L_flare_/L_bol_, is used to indicate the flare activity. We find that, similar to the X-ray luminosity relation, the L_flare_/L_bol_ versus P_rot_ relation can also be described with three phases, supersaturation, saturation, and exponential decay, corresponding to an ultra- short period, a short period, and a long period. The flare activity and the number fraction of flaring stars in M dwarfs rise steeply near M4, which is consistent with the prediction of a turbulent dynamo. The size of starspots are positively correlated with flare activity. The L_flare_/L_bol_ ratio has a power-law dependence on L_H{alpha}_/L_bol_, a parameter indicative of stellar chromosphere activity. According to this relation, a small enhancement in chromosphere activity may cause a huge rise in flare energy, which suggests that superflares or hyperflares may not need an extra excitation mechanism. Through a comparison study, we suggest that flare activity is a more suitable indicator for stellar activity, especially in the boundary region. However, contrary to what is expected, some M dwarfs with strong flares do not show any light variation caused by starspots. Follow-up observations are needed to investigate this problem.