When statisticians divide things into four equal parts, any one of those parts is called a quartile. You might, for example, hear about a successful school that's in the upper quartile of state test scores.
People studying information about how people live — how much money they make, how healthy they are, how much they travel, what their ages are, what TV shows they watch — often separate them into groups for comparison. It's sometimes easier to examine statistics and information when it's divided into quartiles, or fourths. The original use of the word quartile was in astronomy, to mean "ninety degrees apart," from the Latin root word quartus, "fourth."