A TIPS pays a fixed real coupon rate on a principal amount that tracks cpi with a two-month lag. If inflation runs at 3%, the principal grows 3% and the same coupon rate produces 3% more cash. At maturity you receive the greater of the adjusted principal or the original face.
TIPS trade on real-yield-bonds. The difference between a nominal Treasury yield and the TIPS yield of the same maturity is breakeven-inflation, which is the market's inflation forecast and a tradable number in its own right.
Example: you hold $100,000 of TIPS with a 1.5% real coupon. Inflation of 3% lifts the principal to $103,000, so the annual coupon becomes $1,545 instead of $1,500, and the redemption value rises too.
Related: breakeven-inflation, nominal-yield, cpi, inflation-expectations