Ataraxia is a state, not a feeling. The word literally means "without disturbance" — the negative compound of tarachē, agitation. It names the inner condition of the sage: not blissed out, not distant, not anesthetised, simply not pulled around by impressions that should not have been granted assent.
The term is shared across several Hellenistic schools. For Epicurus, ataraxia is the highest good — the state of pleasure understood as the absence of pain and anxiety. For the Pyrrhonist Sceptics (Sextus Empiricus, Outlines of Pyrrhonism 1.25–30), ataraxia is the telos that follows upon suspension of judgment. For the Stoics, ataraxia is a consequence, not a goal — and they more often name the sage's condition with apatheia or eustatheia than with ataraxia. The goal is virtue — living in accord with nature. Ataraxia is what falls out when virtue is sufficiently established, because the disordered pathē are no longer being installed by mistaken assents.
This distinction matters in practice. The Stoic who aims directly at tranquillity often misses it — because aiming at tranquillity makes its absence into a kind of failure, which itself is a disturbance, which is the opposite of the goal. The Stoic who aims at virtue and at the discipline of assent finds, after enough practice, that tranquillity has arrived as a side-effect. Marcus Aurelius's Meditations are partly the journal of a man noticing this — the calm comes not when he reaches for it but when he stops reaching for anything outside his control.
The English word tranquillity sometimes carries connotations of withdrawal or stillness that the Greek does not. The sage in ataraxia may be in the thick of battle, in office, in conversation. The condition is not contemplative repose; it is the absence of inner disturbance, regardless of outer circumstance.