It would be a good idea to read up about the two in the manual... There are 2 major differences with a persistent connection you should be aware of, which can affect server load, and max connections...
Here are the links:
[man]mysql_pconnect()[/man] and [man]mysql_connect()[/man]
It's a good idea to read the user comments below the function descriptions too, because there are a lot of good real world examples of when to do what.