HESI is a series of nursing school competence exams developed by the Evolve-Elsevier textbook company. The exams contain NCLEX-style questions and are supposed to "accurately predict" NCLEX passage rates. There are several different HESI exams: an entrance exam that assesses the student's knowledge of basic academic topics like Chemistry and Math, Small, 50-question exams focused on specific nursing topics (Pharmacology, Med-Surg, Mental Health, etc...), and a 260ish-question exit exam, a comprehensive assessment of any material that should have been covered in nursing school.
The majority of the questions on HESI, like the NCLEX, are application questions that require not only memory of facts but application to patient scenarios and critical thinking. It is not a computer-adaptive test (CAT) like NCLEX, so you take all of the questions regardless of "how well" you answer the questions.
When you complete the test, HESI immediately generates a score and percentile based on the amount of questions you answered correctly and the difficulty of those questions. A score of 850 is generally thought to be the benchmark for NCLEX success, but a score of 900 is recommended.
Many nursing schools require "passing" HESI exams (scoring 850 or higher) in order to pass specific courses or, in the case of the Exit Exam, to graduate.