Vibration motors are used for haptic feedback.
Typical application areas are handheld devices like mobile phones, game controllers, special tools. And in general systems in which the designer wants the feedback to be less obtrusive.
Most vibration motors have an Eccentric Rotating Mass, ERM, this is a weight that is mounted on the shaft of a regular DC motor. This off center mass produces the vibration when rotating. The DC voltage level applied to the DC motor changes the speed of the motor. Which changes both vibration amplitude and vibration frequency of the ERM vibration motor and the surface it is attached to.
There are also vibration motors that are based on the same principle as a loudspeaker these are called Linear Resonant Actuators, similarly to a speaker they need an AC signal to operate. LRAs are tuned to a certain frequency; the resonant frequency. At this resonant frequency the mechanical output is maximal. At other frequencies the output, the vibration, is substantially lower.
Don´t forget a fly-back (protection) diode across the motor, when driving it with a transistor or FET circuit.
Many vibration motors are made for mobile application and have an input voltage of 3V or less. For 5V applications apply a suitable resistor in series, to limit the motor current.
Most LRA vibration motors have a coin shaped housing. But not al coin shaped vibration motors are LRA types. Also some ERM type are coin shaped. You need to check the datasheet for more information. Other common names for this type of housing; pancake or disk type.