Remains of Azure (蒼の残滓 Ao no Zanshi) are the leftover remains of the power borrowed from the Azure from when a person uses a Drive.
Because of the way that a Drive works, the closer the user's soul is to the Azure, then the more powerful the Drive. A trade-off to this is that the Remains of this power cling to the user, the closer to the Azure, then the more Remains. Another way to augment the amount of Remains that attach to the user is by repeatedly using the Drive.
Remains not only cling to their user, but they can also leech onto any person that the user is in contact with. Spinner Superior's incredibly powerful Drive allowed his Remains to cling onto Tadayuki Isa and then to Kana Kirishima, via Tadayuki.
Some Magic can be used to detect the Remains, while some beings, like Raquel Alucard, are capable of innately detecting it.