I use X-Y mode when playing with my analog computers. The AC generates the X-axis by convention because it used to drive a plotter axis. Y was plotted against X. The time/div can be quite slow for real-world problems.

There are cross-coupled differential equations - like the Predator-Prey problem (Lotka-Volterra equations) - where one axis represents the Prey population and the other represents to Predator population. This results in a warped ellipse. It is also useful to just plot each population versus time and, in that case, the X axis can be driven by the AC or just ordinary time/div.

Attached is an analog simulation schematic for MATLAB along with a Y vs time and XY plot of the populations.

XY plots are useful in a number of areas.