"No. It is important."
The gist of it is that combat spheres are condensed power leftover from defeated fiends. Spheres in general are a natural way for pyreflies to arrange themselves in, whenever someone does the work to condense them at all, and the term "combat sphere" refers to those you extract from fiends when you use a certain special spell to do so.
By default, if you literally just grabbed a bunch of pyreflies from a dying fiend and condensed them into a sphere, you wouldn't have anything useful at the end, and you'd more likely than not end up accidentally grabbing the pieces of the souls of the dead instead, which no one wants. What this spell does is separate and order the dissipating pyreflies into useful pieces, defined sort of conceptually in intuitively straightforward ways. And more powerful fiends have more pyreflies tacked on in addition to the souls that make them up and so they typically can generate more combat spheres at the end. And then those combat spheres can get absorbed into your soul and expand your capabilities; that is the main way in which one becomes stronger.
However, you can't just graft spheres onto your soul without limit. It takes a while for the power to become truly yours, rather than borrowed or added on, and if you try to absorb too much all at once you'll end up just losing most of it; your soul won't be able to hold onto it without losing hold of itself and holding onto itself is its main job. The maximum amount of power you can safely absorb at a time is known as your "temporary maximum power", or informally "temp max". The best and quickest way to fully integrate spheres you've absorbed into yourself is through use. Typically, that just means combat, but it doesn't need to; you could in theory absorb a Power Sphere just as well by playing blitzball. It's just that eventually blitzball stops being a challenge in the right way, so you're not really meaningfully using any further improvements you get and so integrating them is slow. Fiends, on the other hand, can become unboundedly powerful, which makes combat always a good way to do it.
That spell is not, technically speaking, the only way to acquire combat spheres. You could make ones the same way you make any other spheres: gather up enough pyreflies, apply your will to them, the end. What that spell does, though, is make this process be very streamlined. Other ways of creating spheres require effort and care and thought; this spell makes use of the extant coherence of fiends, who are already solidified pyreflies themselves and who are already using those pyreflies for their own power, and just redirects that power. It's very efficient and effective, and creates a useful loop for field combatants.
As for the colour of the spheres, those are just built into the spell for ease of categorisation: red ones are standard spheres that improve you in one way or another, yellow ones are sympathetic ones that allow you to share power with someone else, and purple ones are extra-reinforced in a way that allows you to absorb them even if you're already at your temp max because they do the work of staying attached to your soul until fully integrated on their own. Which kinds of spheres a fiend drops is kind of complicatedly determined by the fiend's power and, in a manner of speaking, "personality", since all of magic is so emotions-based. Purple spheres are very rare, whereas red spheres are the most common.