Statcast is a proprietary advanced metrics system that was introduced gradually by Major League Baseball through its subsidiary, MLB Advanced Media, starting in 2015. It is designed to measure all sorts of events that take place during a baseball game by tracking the movements of the ball and of the various players on the field. It was inspired by a system introduced a few years earlier in European football (soccer) that provides a reading on how much distance every player on the field runs during a game, and the speed at which the ball travels. It is in effect an extension of the radar gun readings on pitches that had been a feature of baseball for a number of decades, and the crude measurements of distance traveled by home runs that had also long been communicated to fans.
Statcast provides measurements not just on the speed of every pitch, but also the sharpness of its break and its spin rate (these measurements were actually available a couple of years earlier, through the "PITCHf/x" system), the speed at which a batted ball is hit (exit velocity), the distance traveled, the launch angle, the distance covered by fielders and baserunners and their speed, and the speed of throws made by fielders. More advanced data is also made available to teams. The information is generated through sensors in the ball and overhead high-definition cameras that can track any movement on the field.
At first, this data was a bit of a gimmick, but as a body of statistics was compiled, other uses were found. For example, by comparing the launch angle and speed at which a ball is hit with a database of previously hit balls with similar characteristics, a hit probability can be derived, which can help to measure defensive efficiency, but also whether a hit or homer was the result of skill or luck. This is of course extremely useful in player evaluation. All of what is measured accurately through Statcast was previously looked at by scouts, but through subjective evaluation and not hard numbers. The existence of the data now makes it possible to quantify what used to be simple value judgments (e.g. Player A gets a good jump on the ball, or Player B always has been hitting the ball hard even though he hasn't been getting hits).
The availability of the data generated through Statcast has begun to affect the way the game is played, as, for example, the understanding of how launch angle affects the probability of a batted ball going for extra bases is credited with changing the approach many hitters take at the plate, resulting in a marked increase in homers, but also in strikeouts.