To examine somebody or something is to inspect it closely, hence an examination is a detailed inspection or analysis of an object or person.
In an academic context, examinations (or exams for short) are tests which aim to determine the ability of a student. Exams are usually written although some may be practical or have practical components, and vary greatly in structure, content and difficulty depending on the subject and the age group of the students under test. In some cases diploma is received by those who pass an examination.
See also Driver's license.