What does the MySQL "max_allowed_packet" setting actually control?

According to the page 99 of "Understanding MySQL Internals" (ISBN 0-596-00957-7), here are paragraphs 1-3 explaining it:

MySQL network communication code was written under the assumption that queries are always reasonably short, and therefore can be sent to and processed by the server in one chunk, which is called a packet in MySQL terminology. The server allocates the memory for a temporary buffer to store the packet, and it requests enough to fit it entirely. This architecture requires a precaution to avoid having the server run out of memory---a cap on the size of the packet, which this option accomplishes.

The code of interest in relation to this option is found in sql/net_serv.cc. Take a look at my_net_read(), then follow the call to my_real_read() and pay particular attention to net_realloc().

This variable also limits the length of a result of many string functons. See sql/field.cc and sql/intem_strfunc.cc for details.

This is probably the most complete explanation of max_allowed_packet I have ever seen. I typed those 3 paragraphs right from the book.