The rocks we are concerned with are mainly sedimentary - ie, particles laid down in water over a vast number of years, hardened by induration or some other metamorphic process, and either brought to the surface or mined. Who knows what was in the air at the time of their formation? Particles of all sorts from volcanic eruptions, silty run-off from vast distances away during flooding, etc, etc. So the elemental particles are not 100% pure - they are a mixture to begin with.
In a lot of instances you get ferric or ferrous particles in the original mix. In the case of purple slate from Wales it is not uncommon to see a green spotted or lenticular appearance as ferric reduction takes place around the original iron particle nucleus.
In others slates we find pyrites - scratchy inclusions, 'toxic' or bad if you like.
In others there was some amount of cleavage and cracking during their formation, allowing water bearing other minerals in solution to get into the cracks - the black lines and dots of manganese oxide inclusions in yellow coticules are an example, although harmless or benign, of this type of inclusion.
In geology, the term inclusion is a bit 'loose' inasmuch as it means anything included. However, one type of inclusion known as a 'clast' exists in which we get bits of other, older rocks, etc, in newer rocks. To explain how this happens imagine a silty strata being laid down in a river bed. Further upstream there are rocks that have already undergone full formation/transformation. During a raging downfall torrents of water wash down bits of these older rocks and lay them on the silt layer. The silt layer continues forming for thousands of years, then is transformed itself into rock - with bits of other rock or mineral in it.
Regards,
Neil