It's always handy to see what is written before and after your sentence: "There is something more, if I could find a name for it. God bless me, the man seems hardly human! Something troglodytic, shall we say? or can it be the old story of Dr. Fell? or is it the mere radiance of a foul soul that thus transpires through, and transfigures, its clay continent? The last, I think; for, O my poor old Harry Jekyll, if ever I read Satan's signature upon a face, it is on that of your new friend." "Continent" comes via Old French from the Latin continēns, the present participle of continēre ‘hold together, enclose, contain’ (source of English contain). In this case a clay pot/container.

Continent, as used here, is archaic. It means container, as if to say "its clay body" (body being a sort of container in an abstract sense).