When student performance is to be measured in terms of a specific learning objectives, or criteria, teachers can either use standardized or teacher-made assessments.
Criterion, or performance, based assessments can either be objective, or subjective. It all depends on what content area and on what goals the teacher wishes to test the students. The examples below are only some of many other choices available.
English/Language Arts/Science/Social Studies: Spelling tests and Unit Tests. This type of objective testing is criterion/performance-based because the teacher will create the assessment to specifically test whether the student knows how to spell the words of the week, or whether the student possesses understanding of the unit that has been covered. Students usually fill out objective information to demonstrate mastery of information.
Essay-type tests are also criterion-based tests as long as the teacher has a specific rubric that must be met to achieve a certain grade.
Fact Checks- Using true/false exercises, or chronological events, Science and social studies teachers can test the student's knowledge of specific facts in these two fields, and add to it a chance for the student to write his or her own summary of phenomena as they understand it. Again, rubrics must be in place to determine what type of performance the teacher expects.
Math: Spiral Reviews and Exemplars. - A spiral review is a daily assessment of around 10 Math problems, each testing a different skill that has been covered either the day before, or during the unit. This helps the teacher to quickly identify the areas of weakness and mastery that must be covered during the lesson.
Exemplars are performance assessment and common core prompts and exercises aimed to the development of problem solving skills. They work best when applying the Susan O'Connell problem solving methodology as well as the Polya Four-Step problem solving methods. Exemplars are completely performance-based because the student has to demonstrate in four different steps the understanding of the problem as well as of the strategy that will be used to attempt to solve the problem.
As you can see the key element is to have a clear idea as a teacher of what it is that needs to be tested as demonstration of mastery. That is what makes it a "performance based" assessment.