Mobile IP allows hosts to stay connected to the Internet as they move from location to location. It works by assigning each mobile node a permanent home address and registering their current care-of address with their home agent. When packets are sent to the mobile node's home address, its home agent intercepts them and tunnels them to the node's current location. This allows the mobile node to receive packets while moving between different networks without changing its IP address. Key entities in Mobile IP include the mobile node, home agent, foreign agents, and correspondent nodes. The registration process establishes the binding between a mobile node's home and care-of addresses.