It's different in every state. Back in California when I taught elementary school, it was called the STAR test, but now it's something different. In Washington it's called the WASL. Typically students take the test in spring, around May. The tests usually last about 2 hours a day, for a whole week, depending on age.
For public schools, it's a really big deal because $ is tied to scores. It's really a bad situation for everyone.
I taught at an inner city school in CA where all of my students were English Language Learners and 100% of them were on free and reduced lunch. I had kids enter my classroom directly from Mexico a week before the STAR test, and yet their scores counted against my "total" score as a teacher. That's why the issue of salary being tied to teacher performance as measured by test scores is really scary. I'm all for a pay for performance model, but that's a whole big can of worms.