In baseball, a "brushback pitch," sometimes also known as a "message pitch," is a pitch intentionally thrown off the plate and inside in order to "brush" the batter back away from the plate, thus sending the batter a "message" that he should not lean too far out over the plate.
In baseball, one of the most effective pitches is a pitch thrown down and away from the batter, so most batters try to get as close to the plate as possible so that if a pitch is thrown down and away, they will still be able to reach it. In order to prevent batters from getting too close to the plate and thus neutralizing one of their deadliest weapons (ie pitching down and away), good pitchers find a need to remind batters from time to time why it might be incredibly dangerous to stand too close to the plate (ie the fact that they might get beaned with a 95 mph heater), by deploying the brushback pitch. Basically, pitchers need to keep batters instilled with a healthy sense of fear in order to be most successful.
The difficulty is that the difference between a brushback pitch and a dangerous beanball that hits the batter in the head is often a matter of an inch or two, and sometimes hotheaded young pitchers don't really know the difference. But there is clear a difference in the way the pitches are thrown. To throw a beanball, the pitcher basically just aims at the batter's head (or the spot where he thinks the batter's head will be a moment from now), and throws as hard as he can. But in the case of a brushback pitch, the pitcher actually aims for the inside part of the plate, and then using slight finger pressure, puts a little bit of "run" on the ball so that it will run up and in on the batter late in its path to the plate, but hopefully not too far in. Well executed, this actually adds to the fear as the pitch seems to veer unpredictably inward at the last moment. Throwing a good brushback pitch is a skill, which must be practiced and mastered.
It is often lamented these days that the brushback pitch is a dying art, that Major League Baseball and umpires are too strict and too quick to issue warnings or eject pitchers for throwing what seem to be beanballs without appreciating the fine distinctions between the brushback pitch and the beanball, and thus that many pitchers are "too afraid" to pitch inside and many batters are leaning "too far" out over the plate. But whether this is completely true or more just nostalgia, the ability to pitch off the plate inside when necessary and to occasionally throw a finely placed brushback pitch remain important parts of pitching and pitching well in the Major Leagues today.