Application layer
Postal network: Someone writes a letter to a friend in New York, addresses it, and drops it in a mailbox. The friend opens the letter and reads it with a smile on his face. Neither of them think about how the letter got there -- did it go in a Ford or Chevrolet truck to the airport, what was the name of the person driving the truck, did it fly straight to New York or was it transferred to another plane in Kansas City, etc.? They are working at the application layer -- getting work done. They are communicating directly with each other, unaware of the underlying delivery mechanism.
TCP/IP: A user retrieves a Web page from a server in New York by typing a URL into a browser and clicking the enter key. The server receives the request, finds the page on its hard drive and sends it back to the user. Neither the user nor the client or server software is aware of the way the messages were delivered -- did they go over wireless connections, how many routers did they pass through, who manufactured the routers, was the server a PC or a rack-mounted machine, was it running IIS or Apache, etc.? There are many application layer protocols.
Transport layer
Postal network: If you accidentally write the wrong address on a letter to someone in Kansas, a postal employee in Kansas will stamp it "address unknown" and it will be returned to you. You will also be informed if a registered letter cannot be delivered. You will be unaware of the details of the error message delivery system, and it will be up to you to decide what to do next.
TCP/IP: Transport layer software establishes a connection between a client and server then monitors that connection for errors. It also slows transmission if it gets too fast to handle at the other end. Transport layer software is not concerned with how the data is actually moved from one point to the other -- that is the responsibility of lower level software. There are two transport layer protocols TCP (reliable) and UDP (unreliable, but fast). If TCP tries repeatedly and errors persist, it informs its "boss," the application program.
Internet layer
Postal network: Airplanes move letters between cities. The pilot does not pay attention to who the letters are addressed to or from, what they say, or whether they contain photos and drawings or only written words.
TCP/IP: Internet layer programs move data between networks. IP is the internet layer protocol. IP software ignores the data, and it does the same thing with a packet whether it comes from the Dalai Lama or your mother in law. Once the data gets to its destination local area network (LAN), it is handed over to data link layer software or firmware for delivery to the proper computer.
Data link layer
Postal network: Trucks move letters within a city.
TCP/IP: Data Link layer programs move (incoming and outgoing) data within LANs. Ethernet is the most common data link protocol. A data link program is not concerned with how outgoing data will be handled once it leaves the LAN or how incoming data got there. That is the responsibility of the internet layer software.
Physical layer
Postal network: People use pens and paper to write letters, and the recipient reads them using reflected light and sometimes glasses.
TCP/IP: Physical layer protocols specify the means of representing ones and zeros (bits). The method of transmitting them between two points using wire, radio, fiber, etc. is also specified. There are many ways to make ones and zeros and many ways to transmit them so there are many physical layer protocols.
Breaking the rules
These are ideal descriptions. In real life, a postman might read a letter or decide not to deliver it. On the Internet, a router may be programmed to process packets from the owner of a competing service slowly or to send copies of packets containing certain content to a government security agency. In the postal network, there are laws against tampering with mail. Some people advocate network neutrality laws against differential treatment of packets on the Internet.