Prior to reading this my answer would have been "what does it matter". I'd never thought much about it, and since it really had no bearing on my eternal standing I put the subject aside and put my thoughts and energy towards other things - like work, laundry, dogs, etc. I even had these thoughts upon first encountering this chapter; however, goal-oriented neurotic that I am, I forced myself to read on, rather than skip ahead to the more important chapter "Will Animals, Including Our Pets, Live Again?". I'm glad I did.
Why is Earth's redemption essential to God's plan, you ask? Well, it's the difference between "Extreme Home Makeover" (EHM) and "This Old House" (TOH). For those unfamiliar with these shows, EHM takes a needy family and razes their previous home, whether it needs it or not, and builds them a brand new, big, beautiful, EXTREME home with all new furnishings, appliances, etc with all the latest bells & whistles. Quite often, they even add a new "appliance" to the garage.
TOH takes an old house and restores it to it's original beauty. They remove the remove the stucco from the regal Tudor-style home, the purple aluminum siding from the Arts & Crafts bungalow, and absolutely BAN rust-colored shag carpeting everywhere. Essentially, they "redeem" the home.
God created This Old Earth and, as Alcorn says, redemption is essential because it emphasizes the value our Creator put in to His creation. He will restore His earth to the original Eden that He intended. There is no doubt that parts will be extremely madeover and rust-colored shag carpeting will be sent to the flames of hell (where do you think those sulfuric fumes come from, anyway). But the basic design and framework of His creation will be redeemed to their original beauty and purpose.
Alcorn did a fine job answering the chapter's title question. More importantly, though, God answered my age-old question of "what does it matter?". While it's true that my thoughts on this topic do not have any bearing on my salvation, they do have bearing on my knowledge of my God and Father. This new knowledge of God's care and plan for His creation reminds me of His sovereignty and reinforces to me that He loves me. In recent weeks I've found this to be very comforting as I struggled with some issues in my life. Whether it's EHM or TOH, home improvement can be very laborious. Fortunately, I have a good Carpenter working on me.