What is phase ripple and how is it measured?
I believe it would be more intuitive if the article instead said ...


  the number of ripples which occur in the passband  or normalized frequency of operation.


It can be defined as the deviation of linear phase shift per cycle vs frequency which is useful for units of phase in PM channels instead of time in seconds. 

It can be defined as the derivative of phase shift or group delay in time (s) vs f which is useful for minimizing filter distortion and determine which pole contributes the most signal distortion due to group delay ripple in the passband.

Where bandstop "skirt steepness" is a tradeoff with amplitude ripple in the passband, this GD ripple becomes more prominent yet non-existent in an ideal Bessel response known as the maximally flat group or maximal linear phase response in the passband and Q's &lt;1 are required.

These peaks usually occur due to differences in symmetry or staggered peaks of each stage to equalize the amplitude or GD ripples, whichever is more important.  

The peaks are caused by underdamped resonances or Q>1 which with multiple stages that are  staggered and tuned for equally small passband ripple to achieve steepest skirts for Nyquist filters which demand high rejection at 1/2 the sampling rate to minimize aliasing noise.  These are design tradeoff for BW, sampling rate, amplitude ripple, phase ripple and group delay peaks and thus higher order of the filter to minimize these tradeoff errors.

The number of peaks cannot be more than 1/2 of the reactive (L or C) elements in the equivalent circuit that contribute to phase shift.

If the peaks are not visible in the S21 amplitude response, they are more easily observed in the GD response. 

Below are many variations of an 8th order BPF at 1e3 Hz to show the maximum number is 4 peaks which approaches the Bessel Filter with only 1 peak and minimal GD variation.