This was a question raised by one of the software engineers in my organisation. I\'m interested in the broadest definition.
An application consists of pair of processes which communicate over the network (client-server pair). These processes send and receive messages, into and from the network through a software interface called socket. Considering the analogy presented in the book "Computer Networking: Top Down Approach". There is a house that wants to communicate with other house. Here, house is analogous to a process, and door to a socket. Sending process assumes that there is a infrastructure on the other side of the door that will transport the data to the destination. Once the message is arrived on the other side, it passes through receiver's door (socket) into the house (process). This illustration from the same book can help you:
Sockets are part of transport layer, which provides logical communication to applications. This means that from application's point of view both hosts are directly connected to each other, even though there are numerous routers and/or switches between them. Thus a socket is not a connection itself, it's the end point of the connection. Transport layer protocols are implemented only on hosts, and not on intermediate routers.
Ports provide means of internal addressing to a machine. The primary purpose it to allow multiple processes to send and receive data over the network without interfering with other processes (their data). All sockets are provided with a port number. When a segment arrives to a host, the transport layer examines the destination port number of the segment. It then forwards the segment to the corresponding socket. This job of delivering the data in a transport layer segment to the correct socket is called de-multiplexing. The segment's data is then forwarded to the process attached to the socket.