Thriving describes something that is doing very well — growing, busy, full of life. Its home is in front of a noun: 'a thriving business', 'a thriving city', 'a thriving community', 'a thriving market'. When you say a company is thriving, you mean more than that it is not losing money; you mean it is expanding, hiring, alive. The word carries energy, not just health. It works for living things too — 'a thriving garden', 'a thriving population of birds' — and there the picture is the same: plenty of growth, good conditions. Though actually, most of the time you meet it, it is being used about money and places. 'A thriving little town' and 'a thriving trade' are almost set phrases. Note the double life of the form. It is the -ing form of the verb 'thrive', so 'the business is thriving' is a verb in a continuous tense, while 'a thriving business' is an adjective in front of a noun. Both are correct and both are common; you rarely need to worry about which one you are using.