Certification Exams are a new feature in Fire Emblem: Three Houses.
Certification Exams are a method of class promotion/reclassing. As characters taught by Byleth reach certain proficiencies in different weapons and class types, they are able to change classes by taking a Certification Exam.
Characters must expend seals such as an Intermediate Seal and have a percentage chance to pass the exam. If they are successful, they are able to change into the class.