Inflation Swap Breakevens represent the annualized implied inflation of the headline CPI index as priced into zero coupon inflation swaps traded OTC.
Breakevens are generally believed to be "cleaner" than TIPS derived inflation indications because TIPS incorporate a liquidity (on-the-run vs. off-the run issues + Treasury vs. TIPS) as well as balance sheet premia (being cash instruments). One could see this disconnect quite clearly during 2008 as TIPS were sold by nervous investors in favor of T-bills in search of liquidity and a shortening of duration. Also, unlike TIPS, breakevens have a full term structure with no requred interpolation for benchmark maturities.