During his time on the island, Chuck Noland (Tom Hanks) never opens up a FedEx package, even though they could have made his escape or his survival easier. Why is this?
Tom Hanks's character works for FedEx, and sees it as his job that the package reaches it's intended destination safe and sound, and most importantly unopened. While the package remains closed he still has a chance to deliver it. And delivering it means that he gets off the island.
It was a way of keeping himself sane and keep his hopes up.