First, it reminds us that it's God who saves. He takes the initiative. He follows through. He completes it. He doesn't just make salvation possible, he saves. He takes the first step towards us and enables every step we take toward him. Again, this is so we don't get the credit or the glory. It doesn't depend on us, but on God. Understanding this keeps us from putting trust in our faith. Mark commented that he doesn't see to many people proud of their faith. I agree. Kinda. Here's what I see - I see people who put their faith in their faith, as though it were saving without reference to the object of their faith. Some ask questions like, "Why would God save me and not someone like Gandhi. Is it really just because I said a prayer at church camp one summer?" In essence, this person is putting trust in their confession of faith, as though it was a salvific work. That comes out of a very recent conversation...but I've had dozens like it in the past. Sometimes it's spoken out of doubt - "really, just because I believe, I'm saved?" Sometimes it's false security, "I'm good cause I signed a card at a Cru meeting a couple years ago" or "I went forward at church back when I was a kid".
Different expressions of the same confusion - treating faith as though it was the basis of our salvation rather than the instrument of salvation. It is a form of works righteousness, that says, "Christ lived and died for us. Good. Now all that's needed is my faith and we've got a saving combo!". Understanding faith as a gift given and enabled by the Spirit (through regeneration) keeps us from viewing it as something we've done that contributes to our salvation.
The second reason I think putting regeneration before faith does have to do with evangelism. As I see it, if the Spirit has opened someone's heart, there's nothing I'm going to do to persuade them to repent and believe. It's just not possible to move someone across that decision line, truly, apart from the Spirit's work. So, the pressure is off. On the other hand, if the Spirit is quickening a person, they will respond to the gospel call, and by God's grace, I might have the privilege of being a part of that! So it keeps evangelism in perspective. It gives us hope, even when we don't have persuasive words. It also keeps us from beating ourselves up if someone isn't responding like we want. Finally, it should spur us on to prayer - asking the Spirit to do his work and prepare our friends, neighbors, family members, congregants, etc. to hear the word and enabling them to respond in faith.
Those are my rambling thoughts.