Equipment which contains moving parts, vibrate at a variety of frequencies. These frequencies are governed by the nature of the vibration souces, and can vary across a very wide range or spectrum. For instance, the vibration frequencies associated with a gearbox include the primary frequncies of rotation of the shafts (and their harmonics), the tooth contact frequencies of different gear sets, the ball passing frequencies of the bearings and so on.... If any of these components start to fail, its vibration characteristics change, and vibration analysis is all about detecting and analysing these changes.
This is done by measuring how much the item as a whole vibrates, and then using spectrum analysis techniques to home in on the frequency of vibratin of each individual component in order to see whether anything is changing in the condition of the machine and its different components.