Recent experiments on molecular motor driven in vitro F-Actin networks have found anomalously large strain fluctuations at low frequency. In addition, the shear modulus of these active networks becomes as much as one hundred times larger than that of the same system in equilibrium. We develop a two-fluid model of a low-density semiflexible network driven by molecular motors to explore these effects and show that, relying on only simple assumptions regarding the motor activity in the system we can quantitatively understand both the low-frequency fluctuation enhancement and the nonequilibrium stiffening of the network. These results have implications for the interpretation of microrheology in such active networks including the cytoskeleton of living cells. In addition, they may form the basis for theoretical studies of biomimetic nonequilibrium gels whose mechanical properties are tunable through the control of their nonequilibrium steady-state.