It's the "Graduate Assistant" pass (if you're a TA you can request it online, otherwise you have to go into the office). It allows you to park anywhere south of the river (if you were there for Zoology, Nat Sci is north, BPS/conservatory is south). I usually try to park in the lot closest to the bridge across from Erickson, which is the closest lot to Giltner/Nat Sci south of the river. Usually if you get in before 10, you can definitely find a spot there, but I've always managed to find a spot in a parking lot somewhere in that general area even when I come in later (if you get in at certain times of the day, it requires a little more effort to find one, but I've always eventually been successful). The parking lots I tend to check (38, 40, 41, 56 on busier days) are like 5-10 minutes walking to Giltner/Nat Sci, depending on how quickly you walk, so it's not even taking you that far out of the way.
I think there's a good portion of people who live pretty close to campus so driving isn't as necessary for them; I prefer driving since I'm not much of a biker and I believe the bus ride from my apartment is over 45 minutes.
Feel free to PM me if you have more specific questions.