Before we answer that question, let's keep in mind what exactly we are measuring. Everyone has touched a part of an operating machine (even if it is your car or even your lawn mower) and felt the back and forth movement. Because that movement is 'back and forth', it is defined as cyclical and we call it 'vibration'. Obviously, we would want to somehow measure the amount of back and forth movement. That measurement is known as 'amplitude'.
Frequency identifies how often the movement occurs. What is the significance of frequency? Machines tend to mechanically generate vibration at multiples (harmonics) of their running speeds. For instance, unbalance causes movement (vibration) at a rate of once per revolution (1x RPM). Exactly 1x - not 1.1x, not 0.9x - 1x. A pump with 5 vanes on the impeller can generate hydraulic pulses (which can be measured as mechanical vibration) at 5x RPM - not 4.9x, not 5.1x - exactly 5x.
Phase gives us the Direction of movement at a given moment in the vibration cycle. Phase helps determine how different locations on the machine (different bearings, usually) are moving relative to one another.