The adoption of distributed energy resources (DERs) such as solar panels and wind turbines is transforming the traditional energy grid into a more decentralized system, where microgrids are emerging as a key concept. Peer-to-peer (P2P) energy sharing in microgrids enhances the efficiency and flexibility of the overall system by allowing the exchange of surplus energy and better management of energy resources. In this work, we quantify the resilience enhancement with P2P energy sharing in microgrids by using a novel resilience metric. A standard IEEE 123-node test feeder, integrated with DERs is partitioned into microgrids. Time-series data generated over one year are used to analyze the economic benefits of P2P energy sharing through a cooperative game model. This data is also used in creating a visibility graph to compute the percolation threshold (PT) as a resilience measure. We analyze the impact of P2P energy sharing in three scenarios: within a single microgrid, among neighboring microgrids, and across all microgrids combined within a distribution system. The results show significant benefits, including cost savings of up to $8,380, a reduction in energy dependence on the main grid by 34,917 kWh, and the system's resilience reaching a maximum of 14%. Furthermore, we predict the energy requirements for a microgrid to evaluate its energy resilience for control and operational purposes. Overall, this analysis provides valuable insights into the performance and sustainability of microgrids with P2P energy sharing.