The Java Mail Server project allows clients to connect to a mail server to send and receive emails and attachments. The project is divided into three modules: a server module that uses server sockets to accept client connections, a client module that uses sockets to connect to the server, and an email inbox module that handles mail functions like forwarding, viewing attachments, and saving emails. The server stores details of client connections, mail sending and receiving. Clients can connect when the server is active to exchange emails with other clients. Usernames and passwords are stored in data files rather than a SQL server. The project provides automatic threading to handle socket connections and includes features for reliable TCP communication between clients.