At its most basic level, a test is "standardized" when each test taker is presented with identical sets of questions. Those questions may or may not be presented in the same order (so you might get "Version A" while someone else gets "Version B"), but they will be the same. So if you took one of these tests today, you might get the math section first, while your best friend gets reading.
The purpose of a standardized test is to compare the performance of a broad range of students presented with the same task. The SAT, ACT, and PSAT are all examples of standardized tests.
Why test prep works for standardized tests
Because standardized tests follow a specific structure and assess a standard set of concepts, test preparation can help you succeed on these tests. Test prep is effective because it is an accurate representation of what is on the actual exam, because the format and content are standard year over year. Test preparation also allows you to become familiar with the format, timing, and content before taking the actual exam.
When you know what to expect and how to pace yourself on tests like the SAT, ACT, and PSAT, you're more likely to be relaxed and comfortable, which typically leads to better scores than if you're full of anxiety and stress.
Standardized tests are not just for college admission
To apply to a private high school — or to certain programs in public high schools — you usually have to take an admission exam. These are often standardized, and the most common high school admission exams are the SSAT, ISEE, and COOP. Test prep is beneficial for these tests, too.
Standardized tests are also used by public and private schools to determine how well students have mastered material at a certain grade level. Results can then be used to shape schools' curriculum. Some states require statewide testing more often than others and some states do not require this kind of testing at all.
Test prep is key to success
Just like with a test you'd take in math class, the key to doing well is making sure you're prepared. Standardized or not, good scores are all about the test preparation you put in before test day.