Mysql_connect:
It opens a new connection to the database.
Every time you need to open and close database connection, depending on the request.
Opens page every time when it loaded
<?php
mysql_connect('servername','username','password');
mysql_select_db("db_name");
?>
Mysql_pconnect:
In Mysql_pconnect, "p" stands for persistent connection so it opens the persistent connection.
The database connection can not be closed.
It is more useful if your site has more traffic because there is no need to open and close connection frequently and every time when page is loaded.
<?php
mysql_pconnect('servername','username','password');
mysql_select_db("db_name");
?>