Example: A PSU that filters ripple poorly will cause a CPU and motherboard to run hotter because voltage regulators need to compensate for the low end of the wave. It's even worse for a GPU. If the ripple is bad enough it could cause the CPU to miss cycles altogether and cause a watchdog timer BSOD.
2nd Example: A PSU will poor regulation and hold-up circuitry won't be able to deal with transients. When a sudden load occurs, it might drop the 12v rail below 12v, where a good PSU can hold up to a large load transient and consistently hold 12v on the rail. Running less than 12v to your graphics card is really bad. It will cause driver crashes, artifacts, the graphics card will run hotter, and shorten the life of the card.
I'm not sure how good your electrical theory knowledge is, but study up on what a capacitor and an inductor does, how filters work, AC to DC rectifier, how a transformer works, and what a time constant is. All that is basically how a PSU works, although now it's more digital.