Sparks of holiness is the Divine energy that exists within every created thing, that constitutes its essence and soul.
Kabbalist Rabbi Isaac Luria (the "Ari", 1534-1572) taught that no existence is devoid of a Divine spark. Nothing can exist without the pinpoint of the Divine presence (Shekhinah) that imbues the created with being and purpose. When a person utilizes something toward a Divine means, he brings to light this Divine spark, manifesting and realizing the purpose for which it was created.
In all physical substances, a material "husk" (Qliphoth) encases and conceals the divine spark at its core, necessitating great effort on the part of man to access the spark without becoming enmeshed in the surface materially. Not every spark, though, can be actualized. There are certain "impregnable" elements whose sparks are inaccessible to humans. When the Torah forbids something, it means that its husk cannot be penetrated. Therefore, its spark remains locked within and cannot be elevated.