Amplitude is the measure of the strength of a wave.
Since there are many types of wave, their amplitude has to be measured in different ways.
An abstract sine wave on a sheet of graph paper can be characterized by its maximum height above the x axis. The simplest, 
, has an amplitude of +/- 1. The class of "real" waves that are sine-like can be similarly measured, for instance, water waves on the ocean or a lake. It is important to differentiate between measuring the displacement from rest versus the peak-to-peak distance.
Sound waves can be expressed as a difference in pressure between their peak compressions and rarefactions, or, more practically, by their loudness or sound pressure level.
An earthquake is (usually) a longitudinal wave in the surface of the earth, and while the motion back and forth can be measured, their strength is usually expressed on the Richter Scale.