The tail at a Treasury auction is the difference between the highest yield accepted at the auction (the "stop") and the yield at which the security was trading in the when-issued market just before the auction. It is reported in basis points.
Tail size matters relative to history. A 1 bp tail on a 2-year note auction is more significant than a 1 bp tail on a 30-year bond auction because the shorter-maturity market is tighter. The auctions tool normalizes each tenor's tail against its own historical distribution.
Tails are among the most closely watched auction metrics because they provide a real-time read on demand that isn't available from the bid-to-cover ratio alone. A high bid-to-cover can coexist with a positive tail if bidders are concentrated at lower prices.
Large positive tails (3+ bps) can trigger immediate selloffs across the curve, while negative tails often spark rallies.