Eudaimonia is the standard Greek philosophical term for the flourishing human life — the life that goes well in the deepest sense, not merely the life that feels good moment to moment. It is sometimes translated as happiness, but the modern English connotation of subjective pleasant feeling misses the weight of the Greek. Eudaimonia is a condition of the life as a whole, not a feeling at a time.
Every Greek philosophical school had its account of eudaimonia. Plato and Aristotle identified it with virtue and the contemplative life (with various refinements). Epicurus identified it with pleasure (specifically, with the absence of pain and anxiety). The Stoics identified it with virtue, full stop. The Stoic eudaimōn is the virtuous person. The vicious person, no matter how prosperous, is not eudaimōn. The virtuous person, no matter how impoverished or ill or disgraced, is.
This is the strongest version of what philosophers call the self-sufficiency thesis. Most people, asked whether a virtuous person being tortured to death is eudaimōn, will say no. The Stoics say yes. They are aware that this strikes most people as paradoxical. The strength of their position is its consistency — once you grant their theory of adiaphora and the goodness of virtue, the conclusion follows. The cost of their position is that it requires you to grant a theory most people will not grant.
For the practitioner, the working interpretation is more modest. The Stoic claim that virtue is sufficient for eudaimonia may or may not be granted. But the weaker claim — that virtue is necessary for eudaimonia, and is the only part of the formula entirely up to you — is much harder to deny. And it is enough to organize a life around. It also gives virtue its place as the Stoic telos. Practice the discipline of the soul; cultivate virtue; hold the externals with the reserve clause (hupexairesis). Eudaimonia, whatever it turns out to be exactly, will not be reached any other way.