I Listened to a podcast, in which the speaker attempted to explain what тренироваться на кошечках means and how it's used, yet I failed to grasp the meaning. Can someone explain?
Means "to train on a dummy" or "to practice the skills on a much simpler case".
Having been born back in the USSR and still being widely used by all generations, except may be the very old, it's quite a resilient meme from a film called "Операция Ы". Here's the scene where it's used: link.
It can be employed quite liberally in all sorts of conversations -- you can have a dialogue that goes like this:
-- Давай поднимемся на Эверест?
-- Может, сначала потренируемся на кошечках и покорим Эльбрус?