JEE (Joint Entrance Exam) is a national level undergraduate entrance exam for Engineering. The exams are of the objective pattern. JEE is an examination through which one gets admitted to the IIT, which is a college . It is constituted by two different examinations - JEE Main and the JEE Advanced.
The erstwhile AIEEE exam will now be called as JEE-MAIN exam and erstwhile IIT-JEE will now be called as JEE-ADVANCED exam.
Check JEE wikipedia for full detials