Development of PHP's MySQL extension (which provides all the mysql_* functions) ceased several years ago, and does not take advantage of any features added to MySQL since MySQL 4.1.
PHP's developers recommend that this extension no longer be used for new development. It has been outdated since PHP 5.0, deprecated since PHP 5.5, and removed from PHP 7.0.
This does not mean that MySQL support was removed. That would be silly.
Years ago (around 2002-2004), all development of PHP's MySQL interface was shifted to the MySQLi and PDO::MySQL APIs, and all new development should use one of these; existing applications using the MySQL interface should be migrated as soon as it's feasible.
Development of the MySQL extension ended at the same time, and had since only had maintenance work done on it to keep it functioning while the rest of PHP changed around it. And got really boring. PHP's developers had better things to do than keeping an outdated extension ticking over, just as Microsoft has better things to do than supply updates for Windows 95.
All manual pages for functions in the old API ([man]mysql_connect[/man], [man]mysql_query[/man], etc.) have warnings about this, and include references to suitable replacements.
It is recommended to use either the [man]mysqli[/man] or [man]PDO_MySQL[/man] extensions. It is not recommended to use the old mysql extension for new development.
This extension is not recommended for writing new code. Instead, either the mysqli or PDO_MySQL extension should be used.
Someone at Oracle (the owners of MySQL) has written a migration note (https://wikis.oracle.com/display/mysql/Converting+to+MySQLi), which includes a converter intended to ease the process. (Fair warning: I personally haven't used it, so I don't know how effective it is; it was published in December 2011. While I'm on the subject of fair warnings, I should point out that I generally don't use the MySQL DBMS anyway; I'm just collecting news from other sources here.)