Back extension is a strength training

Strength training

Strength training is the use of resistance to muscular contraction to build the strength, anaerobic endurance, and size of skeletal muscles. There are many different methods of strength training, the most common being the use of gravity or elastic/hydraulic forces to oppose muscle contraction...

 exercise. It is done for strengthening lower back muscles.

Using equipment, it can be done by lowering the body from a stand and raising back using the roman chair

Roman chair

The Roman chair is a piece of exercise equipment. The equipment is mainly used for the lower back, but can also target the gluteal muscles and the abdominals. How the equipment is defined, and what the 'Roman chair exercise' is specifically, is an issue that is not clear.-Exercises:Various...

, or using a back extension machine where body pushes a weight backwards.

Without using equipment, it is done by lying face-down on the floor, and lifting the torso and arms together up off the floor. This is also called hyperextension

Hyperextension (exercise)

A hyperextension is an exercise that works the lower back as well as the mid and upper back, specifically the erector spinae....

.