You can think of a hardy perennial as the plant that will not be got rid of. Winter comes, the top dies back, the pot looks empty — and in spring green shoots push up again without anyone doing a thing. Cut it down and the same thing happens next year. Each half of the name carries one part of that picture: hardy is the cold it survives, perennial is the coming back. Once you hold that image, the second use follows on its own, because some subjects behave exactly like that plant.