Where the privacy comes from
On a public chain, your address is your history. Anything you buy, anyone can read: your size, your timing, your other coins, your profit. Veil puts one hop in the middle. Your wallet pays our desk. The desk buys. The coins are delivered to an address that has never done anything before. On chain there is no line from your wallet to that address — only a payment to a desk that thousands of payments go to, and a delivery from a desk that makes thousands of deliveries.