The Continent is the territory to the east of Prythian.
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The Mortal Queens express that if a war against Hybern should break out, they will protect the Continent and its people, but the southern territories of Prythian, where Feyre's family lives, will be left defenseless despite being part of the mortal realms.
When Feyre visits her family, her sister Elain tells her that one day they could go to the Continent to find more flowers for their garden. Feyre's father later travels to the Continent for business reasons.