session_register creates global variables (e.g. $var as opposed to $SESSION['var']). It is, however, depreciated as it doesn't work on a system where register_globals is disabled (the default in PHP since about halfway through v4's life), and it has the same security deficiencies that register_globals has. Using $SESSION assures that anything in that superglobal is something you explicitly put in there.
In general, there's no real advantage to using session_register, and it's bad practice to do so since it doesn't work in a very large number of setups.