The ACT is a standardized test designed to show colleges how prepared you are for higher education by measuring your reading comprehension, knowledge of writing conventions, and computational skills, and then comparing you to the rest of the high school students who take it.
The exam essentially serves as a nationwide college admissions test (though it's far from the only factor schools consider when looking to admit students).
Most four-year schools require applicants to submit either ACT or SAT scores (they don't distinguish between the two), which can then make up as much as 50% of the admission decision. A strong standardized test score is a key part of your application.
There are also a lot of students who are required to take the ACT by their high school. Utah uses the ACT as a statewide assessment test, so every junior at a public school takes the ACT.