The correct answer is option 'C' - vibration.

Explanation:
Motion refers to the change in position of an object with respect to its surroundings. When an object moves back and forth in a repeating pattern, it is said to exhibit to and fro motion. This type of motion is characterized by the object oscillating or vibrating between two points.

Vibration is defined as the rapid to and fro motion of an object about an equilibrium position. It involves the object moving back and forth repeatedly in a periodic manner. The object undergoes a cycle of motion where it moves away from its equilibrium position, reaches a maximum displacement, and then returns to its original position. This cycle of motion is repeated continuously.

Vibration can occur in various forms and can be observed in different objects and systems. Some common examples of vibration include the swinging of a pendulum, the back-and-forth motion of a spring, the shaking of a guitar string, or the oscillation of a tuning fork.

The motion of vibration can be described by several parameters:

1. Amplitude: The maximum displacement or distance traveled by the object from its equilibrium position during vibration.
2. Frequency: The number of complete cycles or oscillations the object undergoes in a given time period.
3. Period: The time taken for one complete cycle or oscillation.
4. Phase: The position of the vibrating object at a specific point in time during its cycle.

Vibration is a fundamental concept in physics and is closely related to the behavior of waves. Waves can be defined as the transfer of energy through a medium without the transfer of matter. They can be categorized into mechanical waves (requiring a medium for propagation) and electromagnetic waves (not requiring a medium). Vibration is a type of mechanical wave.

In conclusion, the to and fro motion of an object is called vibration. This motion involves the object oscillating or vibrating between two points in a periodic manner. Vibration is characterized by parameters such as amplitude, frequency, period, and phase.