Something that's thriving is doing very well. You have a thriving cupcake business if you can hardly bake enough to keep up with your customers' orders.
Use the adjective thriving to describe something that's healthy — like your new puppy — or profitable and busy — like your dad's car dealership. A thriving Mexican food truck always has a long line in front of it, and a thriving publisher puts out many popular books. Thriving comes from the verb thrive, and its Old Norse root word, þrifask, which means both "thrive" and "grasp to oneself," from þrifa, "to clutch or grasp."