Lateral pushups are an interesting style of pushup that should be incorporated into any fitness routine. The pushup itself is one of the simplest, yet most versatile bodyweight exercises for developing full body strength.
You read that right, most people see pushups as an exclusively upper body exercise, which is not the case. Many people use different variations of pushups to work the entire body, such as the Hindu (or divebomber) pushup, Aztec pushup, handstand pushups or Lalanne pushups, among others.
Lateral pushups are one such variation; done correctly, they can work the core, the arms, the chest, the back, and the shoulders. In fact, this one particular pushup variation helped my uncle, who suffered from a 30+ year old shoulder injury, regain much of the range of motion in his shoulder. I hope that it serves you well in your training!