TL;DR: "Descent of Avernus" is an allusion to Virgil's Aeneid. In context in Carmilla, where the narrator Laura is describing her slide into a mysterious illness or ‘fascination’, it has the implication that it will be easy for her to succumb to the malady and difficult for her to escape.
The Oxford Classical Dictionary says:
Avernus, a deep volcanic crater, now a lake, near Puteoli. Its appearance inspired the belief that it led to the Underworld.
In book VI of Virgil's Aeneid, the Trojan prince Aeneas visits the Underworld to speak with his dead father Anchises. The Cumaean Sybil had previously warned him that the Underworld is easy to enter but hard to leave:
Tros Anchisiade, facilis descensus Averni;
noctes atque dies patet atri ianua Ditis;
sed revocare gradum superasque evadere ad auras,
hoc opus, hic labor est.
Trojan, son of Anchises, the descent of Avernus is easy;
Night and day the dismal doors of Dis stand open;
But to reclimb the stair and escape to the breezes above,
That is toil, that is labour.
(Some manuscripts of the Aeneid have descensus Averno, the descent into Avernus.)
This is one of the most well-known passages in the Aeneid, and the descent of Avernus is widely used to mean that it is easy to slide into evil or into disaster, and hard to get out again.
The decline in frequency of "Avernus" in the Google Ngram results is just a consequence of the general decline of classical reference. In the 19th century, the Greek and Latin classics were a pillar of the education of the middle and upper classes, hence a natural source of allusions and quotations. Not so much now.