ZiPS is a system of player projections developed by ESPN's Dan Szymborski when he was at Baseball Think Factory. According a Q&A on the Baseball Think Factory website, ZiPS uses growth and decline curves based on player type to find trends. It then factors those trends into the past performance of those players to come up with projections.
The system uses statistics from the previous four years for players from ages 24-38, and it weights more recent seasons heavier. For younger or older players, it uses weighted statistics from only the previous three years. The system also factors velocities, injury data and play-by-play data into its equations.
Like other projection systems, ZiPS uses past performance and aging trends to develop a future projection for players. On Fangraphs, the projections are updated daily and predict each player's numbers over the course of the remainder of the season.
Obviously, no one is claiming that every ZiPS prediction will come true, but it is widely regarded as one of the most accurate predictors in the industry.