I live in Florida and have no idea what this is.

That's called hen and chicks
Sempervivum is the Latin name

Pronunciation: \-lənt\
Function: adjective
Etymology: Latin suculentus, from sucus juice, sap; perhaps akin to Latin sugere to suck — more at suck
Date: 1601
1 a: full of juice : juicy b: moist and tasty : toothsome <a succulent meal> cof a plant : having fleshy tissues that conserve moisture
2: rich in interest
— suc·cu·lent·ly adverb

Main Entry: 2succulent
Function: noun
Date: 1825
: a succulent plant (as a cactus or an aloe)

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