the distance x is the amplitude of the wave. Sometimes that distance is called the "peak amplitude", distinguishing it from another concept of amplitude, used especially in electrical engineering: the root mean square amplitude, defined as the square root of the mean of the square of the maximum vertical distance of this graph from the horizontal axis.
There are a few ways to formalize amplitude:
to do: compare when/how these are equivalent or not, and when to use them
In the simple wave equation
The amplitude of a wave is the measure of the magnitude of the maximum disturbance in the medium during one wave cycle, and is measured in units depending on the type of wave. For examples, waves on a string have an amplitude expressed as a distance (meters), sound waves as pressure (pascals) and electromagnetic waves as the amplitude of the electric field (volts/meter). The amplitude may be constant (in which case the wave is a c.w. or continuous wave) or may vary with time and/or position. The form of the variation of amplitude is called the envelope of the wave.