To get these functions to work, you have to compile PHP with --with-imap. That requires the c-client library to be installed. Grab the latest version from ftp://ftp.cac.washington.edu/imap/ and compile it.
Then copy c-client/c-client.a to /usr/local/lib/libc-client.a or some other directory on your link path and copy c-client/*.h to /usr/local/include or some other directory in your include path.
Note: Depending how the c-client was configured, you might also need to add --with-imap-ssl=/path/to/openssl/ and/or --with-kerberos into the PHP configure line.
Note that these functions are not limited to the IMAP protocol, despite their name. The underlying c-client library also supports NNTP, POP3 and local mailbox access methods.
This document can't go into detail on all the topics touched by the provided functions. Further information is provided by the documentation of the c-client library source (docs/internal.txt). and the following RFC documents:
RFC2821: Simple Mail Transfer Protocol (SMTP).
RFC2822: Standard for ARPA internet text messages.
RFC2060: Internet Message Access Protocol (IMAP) Version 4rev1.
RFC1939: Post Office Protocol Version 3 (POP3).
RFC977: Network News Transfer Protocol (NNTP).
RFC2076: Common Internet Message Headers.