Chandelle: The objective of this maneuver is to develop the pilot's coordination, orientation, planning, and feel for maximum performance flight, and to develop positive control techniques at varying airspeeds and attitudes.
Lazy Eight: The objective of the lazy eight is to develop the pilot's feel for varying control forces, and the ability to plan and remain oriented while maneuvering the airplane with positive, accurate control. It requires constantly changing control pressures necessitated by changing combinations of climbing and descending turns at varying airspeeds. This is a maneuver often used to develop and demonstrate the pilot's mastery of the airplane in maximum performance flight situations.
Taken from FAA-H-8083-3 (Airplane Flying Handbook, since you probably don't have one)