BRST symmetry is a property present in various kinds of quantum mechanical equations (which is quite mathematically and geometrically challenging), in which one kind of a non-physical output of the equations cancels out another kind of non-physical output of the equations, making the equations "renormalizable" (i.e. possible in principle to calculate without blowing up into infinities). In the context of QCD, another way to put this is that "all the UV [i.e. high energy] divergences of the theory can be cancelled by the counterterms[.]" This symmetry appears to be present even in the non-abelian gauge fields of the weak force and strong force equations, although this reality may need footnotes for exceptions in certain special cases. This was described theoretically in the 1970s, but apparently, since then this insight hasn't done much besides assuaging concerns that renormalization didn't have a mathematically rigorous basis.
The theoretical program involved in working with the BSTR symmetry also provides a theoretically sound alternative to the Feynman path integral conceptualization of quantum mechanics, that is rather more conceptually challenging to grok, but generalizes to cases more complex than QED in Minkoski spacetime more naturally.