Functionally speaking, ash is the leavings of fire. Its what isn't consumed by a burn, and those things that remain are always transformed by flame. This act of transformation leaves an imprint, both in the literal sense (scorch marks, soot, embrittled material) and in the magical as well as we hear and understand through the axiom as above, so below.
When something has been reduced to ash by and through the act of magic, that which has been consumed by flame becomes an extension of your intention and will. Your magic and your essence have fused with the material as it has been caressed by flame, and so what remains should be seen as the culmination of your efforts so far.
Thus, if you perform a ritual of blessing and goodwill, the ash that remains is naturally attuned towards this frequency and can be used as an ingredient within following works. Likewise, if your works intend to make something fruitful, then the ash that remains can be seen to have a like capacity and intention.
Put that back into your magick.
That's literally a gift you've made for yourself, so be sure to use it in rituals of like intention and aims. ;)
Sit with that this Full Moon weekend and contemplate how else to use this advice in your Works. There are many ways to get clever with this!