Hi dutchgirl!
I'm going to guess that the tradition stemmed out from a desire to help the newest members feel welcome. It also could be so that the new members could have things with the sorority's name, letters, mascot, whatever--again, so she would feel a part of the sisterhood. It's so much fun to be able to wear a sweatshirt given to you from your big sister
Some of it is tradition. Gifts are never supposed to overshadow the real reason we have big sisters/mothers/sister-moms/sponsors though. The big sister is there to be a friend to the new member, the person she can come to with any questions or anything at all. The big helps her little through her new member education and ensures she's learned everything she needs to be a fully initiated member of the sorority. It's a bond that can honestly last a lifetime!
HTH,
Christin