Douglas Comer defines a protocol as "a formal description of message formats and the rules two or more machines must follow to exchange those messages."
Protocols usually exist in two forms. First, they exist in a textual form for humans to understand. Second, they exist as programming code for computers to understand. Both forms should ultimately specify the precise interpretation of every bit of every message exchanged across a network.
Protocols exist at every point where logical program flow crosses between hosts. In other words, we need protocols every time we want to do something on another computer. Every time we want to print something on a network printer we need protocols. Every time we want to download a file we need protocols. Every time we want to save our work on disk, we don't need protocols - unless the disk is on a network file server.
Usually multiple protocols will be in use simultaneously. For one thing, computers usually do several things at once, and often for several people at one. Therefore, most protocols support multitasking. Also, one operation can involve several protocols. For example, consider the NFS (Network File System) protocol. A write to a file is done with an NFS operation, that uses another protocol (RPC) to perform a function call on a remote host, that uses another protocol (UDP) to deliver a datagram to a port on a remote host, that uses another protocol to delivery a datagram on an Ethernet, and so on. Along the way we made need to lookup host names (using the DNS protocol), convert data to a network standard form (using the XDR protocol), find a routing path to the host (using one or many of numerous protocols) - I think you get the idea.
One of the challenges facing network designers is to construct protocols that are as specific as possible to one function. For example, I consider NFS a good protocol design because one protocol does file transport (NFS), one protocol does procedure calls (RPC), etc. If you need to make a remote procedure call to print a file, you already have the RPC protocol that already does almost everything you need. Add one piece to the puzzle - a printing protocol, defined in terms using the RPC protocol, and your job is done.
On the other hand, I do not consider TCP a very good protocol, because it mixes two functions: reliable data delivery and connection-oriented streams. Consequently, the Internet lacks a good, reliable datagram delivery mechanism, because TCP's reliable delivery techniques, while effective, are specific to stream connections.