Socket programming in Java allows applications to communicate over the internet. Sockets are endpoints for communication that are identified by an IP address and port number. A socket connection is established between a client and server socket. The server creates a welcoming socket to accept client connection requests, then a separate connection socket to communicate with that client. Data can be sent bidirectionally over the connected sockets as input/output streams. UDP uses datagram sockets without a connection, requiring the explicit destination address on each message.