Both norm-referenced testing and criterion-referenced testing seek to assess students; however, they differ in what they are measuring.
Norm-referenced testing seeks to rank students based on test achievement. Essentially, norm-referenced testing is comparing a student's score against the scores of the thousands of other students that have taken the test. If a student scored better than everybody else that took the test, it would be equivalent to an athlete getting the gold medal in the Olympics. It's important to note that norm-referenced testing doesn't necessarily accurately show student learning and mastery of skills. It simply shows how a student stacks up against other students that have taken the test. This is why it is generally important to have a large sample pool of students taking this kind of test.
Criterion-referenced testing attempts to measure the skills and knowledge that a student has mastered. Generally, the score is given as a percentage. For example, if a test has 100 questions, and the student gets 99 of them correct, the student scores a 99%. This kind of test can be given to small groups or large groups because it isn't comparing students to each other. The test is assessing student learning against predetermined criteria or learning standards. Generally speaking, tests and quizzes that a classroom teacher gives to classes over the course of the school year are this kind of test.