1- Directional Antennas have higher antenna gains. So, in essence the received signal strength is higher. Hence the received SNR gets improved w.r.t a link with Omni-directional antennas. From Shannon's famous formula, higher SNR translates to higher throughput.
2- Directional antennas have limited interference footprint in the spatial domain w.r.t to Omni directional antennas. This feature allows spatial re-use. Hence, the average network spectral efficiency is improved with careful protocol implementation. To see the theoretical effect on the network throughput you can read on scaling laws of ad-hoc network with and without directional antennas. See the attached link.
A summary of the main result is that in arbitrary networks ,the capacity of networks using directional antennas will be improved by a factor of 2π√αβ, where α and β are the beamwidths of transmission and receiving directional antennas ,respectively.