TIPS are Treasury Inflation-Protected Securities, US government bonds whose principal is adjusted in line with consumer prices. Because that adjustment removes the inflation component, the quoted TIPS yield is a market-observed real yield, and real yields are the primary macro measure of the opportunity cost of holding non-yielding gold.
Gold traders take two numbers from the TIPS market: the real yield itself, and breakeven inflation, calculated as the nominal Treasury yield minus the matched-maturity TIPS yield. Separating these distinguishes an inflation-expectation story from a tightening-policy story, which is essential because rising breakevens with stable real yields has historically been a far friendlier backdrop for XAUUSD than rising real yields.