This equation computes the amplitude of a simple harmonic oscillator, the maximum displacement experienced by the body in its oscillating motion.
When the restoring force is directly proportional to the displacement from equilibrium, the oscillation is called Simple Harmonic Motion (SHM).
Young, Hugh and Freeman, Roger. University Physics With Modern Physics. Addison-Wesley, 2008. 12th Edition, (ISBN-13: 978-0321500625 ISBN-10: 0321500628 ) Pg 427, eq 13.19