What is a good teaching example/application for jagged arrays (2d arrays with irregular row lengths)?
Hmm, here are a few ideas:


Calculating student GPA where the grades are all stored in an array of arrays, and the different semesters have different numbers of courses.
Make a lookup table of prime factors.
Consider an array of arrays of paths to hike, and local maximum / local minimum elevations passed along the way. Since there will be a different number of local maxima/minima along the way, the array will naturally be jagged.  Figure out which hiking path involves the least climbing.
Same as above, but now instead store the elevation every x number of meters.  Since the hiking paths are somewhat different lengths, the array will naturally be jagged.  Determine which path has the lowest average slope for a hiker who has difficulty with hills.
(More advanced than AP, probably) Many Sudoku variants often suggest jagged arrays.


Also, for what it's worth, if you organize your midi-like events by time, it's actually ragged.  Different numbers of notes are played (or stop playing) at different times.  If you play a triad, you will have three events.  If you play a triad at the same time as you stop playing a previous melodic note, you now have four events.