the general problem with register_globals is that it will put into your webpage whatever is in GET.
example:
if your program expects some variable from POST, and it is not there, it will automatically look for it in GET. so if you have a script that handles a form... and i know where it is... i can force variables into it by directly accessing it in the address, which will not have a post associated with it so php will use whatever is in GET.
as philipolson suggested, this does not have to be insecure, but leaves the door open for the writing of insecure code by you in an unattentive moment.
as PHP is moving to be more and more legit, it wants to close the doors to things which make it more easily misused.