Ok. I'll explain it this way. Under non-persistent connections every time you request a wwwthreads page the script has to make the connection to the sql server, connect to the database and then disconnect when finished. Meaning basically a connection is only made to the SQL server when needed. Natually, there is a bit more overhead in doing this.
Under persistent connections, once a connection is made to the database it remains open. This connection is available for all subsequent requests that WWWThreads make. No overhead for connecting/disconnecting for each script.
So, the second way, using persistent connections is faster. But here is the drawback. A connection is left open for every webserver processes that runs one of the wwwthreads scripts. On a typical system you may have anywhere from 10 to a couple hundred webserver processes running. And during the course of your browsing session you will hit a wide variety of those webserver processes. So, if you hit one that doesn't have a connection open to the db it connects and then leaves it open. So, as you can see after a while you may have a mysql connection open for every webserver process running. Isn't a big deal if it's your own system, but if this is a shared server then they probably wouldn't like this too much.