It's up to the individual school. An increasing number of schools are using this test (or others) to assess their students at diffferent stages of their programs. Some just use it as a diagnostic assessment to give the students and faculty an indication of whether or not they are on track to be successful in passing the NCLEX. Other schools are requiring students to achieve certain scores in order to progress from one level to the next (or to graduate).
I had to take the HESI when I was in undergrad. That was almost two years ago. You weren't able to graduate without passing it and walk in the spring graduation otherwise, supposedly. We saw it as a way for the school to increase their NCLEX pass rate by holding back some who might not pass the Nclex the first time because it would take them out of the numbers statistically. That was our theory atleast. We were never told about the test when applying, only in our second or third semester did they mention it. We were only the second class in our college to take it.