The Multipeer Connectivity Framework supports discovering and communicating with nearby iOS devices via Wi-Fi and Bluetooth, but is not compatible with Android. The framework includes several classes such as MCPeerID for identifying peers, MCAdvertiserAssistant for handling service advertising, and MCBrowserViewController for inviting nearby peers to sessions. It allows for reliable or unreliable data transmission among connected peers in a session, addressing various use cases such as real-time data sharing.