It would be a plant that is capable of persisting for at least three annual growth cycles & that does not become highly lignified (woody). In most US zones, it would be a plant with fleshy stem parts that dies back to the ground in winter.

Al

Thanks again for your help Al! I'll be a little more assured that non-indigenous plants (rangoon creeper to TX) will perform like a perennial. Just wanted to make sure, because I don't want to have to replace the plant every year.

"herbaceous perennial" just describes a plant's manner of growth, not necessarily its hardiness. While Quisqualis IS technically a perennial, it is a tropical perennial and may behave like an annual in colder climates. It is listed only as hardy to zone 9 so your success with overwinering it could be iffy.