It means someone, somewhere, has to look at balances now and then go back (on the blockchain) and 'delete' old transactions where addresses have a zero balance now.
Correct me if I miss-understood something but this sounds like centralization?
No, we devise a system where the blockchain's state is being frozen every 10000 blocks (or any number that makes sense). Now we only redistribute that small blockchain to 'reduced' nodes. They could still be sure that blockchain is a correct copy by comparing it's hash or merkle sum or whatever to other instances. That way we wouldn't have to download the whole freaking chain, which doesn't make sense for various applications. Light wallets don't rely on downloading the whole chain already.