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Because Epicureanism fell out of favour for so much of history there are many Epicurean terms which either have not become common parlance or whose meaning is not immediately apparent. Even the term Epicurean itself has been distorted. Here is a list of some of the more useful terms which appear in Epicurean studies. Feel free to add more in the comments. Hope all is well.
Aponia – An absence of pain. For Epicurus pleasure was maximised when you no longer experienced any pain.
Ataraxia – A state of profound tranquillity. Ataraxia is achieved when you have no more worries or fears at all.
Apatheia – The Stoic analogue of Ataraxia. Apatheia is the state of mind achieved when the passions are controlled, perhaps even entirely removed.
Clinamen- This is the term given by Lucretius which describes the random motion of atoms in a void. In the atomic theory of the Epicureans without this random swerving then atoms would not have been able to form larger objects by collision. The random swerve also prevents the universe from being deterministic.
Epicurean epistemology – Epistemology is the study of truth and knowledge. How do we know what we know? Epicureanism has three main routes to knowledge. Sensations (aisthêsis) are the information our sense organs receive and refer to the mind. These are always right, though we may misinterpret what we are sensing. Preconceptions (prolepsis) are those ideas which all people share, universal ideas. Feelings (pathê) are those things which are true for us, our own sense of pleasure for example. A square of very dark chocolate may make me happy but it is not a universal experience.
Eudaimonia – An objective goal of a philosophy. Eudaimonia can be translated as ‘good spirited.’ Eudaimonia is the state a philosophy aims to place its practitioners in, a state in which they are flourishing. It varies from philosophical school to school but for Epicureans Eudaimonia is pleasure (as understood by Epicureans, see Hedonism).
Gods – Epicurus was parodied by other philosophers as being an atheist. His surviving letters show that he did believe in gods, but perhaps not in a way they or we would recognise. The gods of Epicurus were beings within the universe, composed of atoms, and utterly unconcerned with human affairs. They lived lives of ataraxia and aponia.
Hedonism – Named for the goddess embodiment of pleasure – Hedone. Hedonism is the pursuit of pleasure. There are many schools of hedonistic philosophy, of which Epicureanism is one. Hedonism can be the mindless chasing of any pleasurable activity or a more refined study of the maximising of pleasure in a rational manner. Epicurus explains some the possible confusions hedonism can imply-
When we say . . . that pleasure is the end and aim, we do not mean the pleasures of the prodigal or the pleasures of sensuality, as we are understood to do by some through ignorance, prejudice or wilful misrepresentation. By pleasure we mean the absence of pain in the body and of trouble in the soul. It is not by an unbroken succession of drinking bouts and of revelry, not by sexual lust, nor the enjoyment of fish and other delicacies of a luxurious table, which produce a pleasant life; it is sober reasoning, searching out the grounds of every choice and avoidance, and banishing those beliefs through which the greatest tumults take possession of the soul.
—Epicurus, "Letter to Menoeceus
Katastematic pleasure – Literally - Pleasure at rest. A katastematic pleasure is a pleasure one feels from ‘being.’ So aponia is the katastematic pleasure one feels when you are without pain.
Kinematic pleasure- Literally - Pleasure in motion. Kinematic pleasures are derived from ‘doing.’ The pleasures of eating, drinking, conversation, those derived from the senses.
Otium – A Latin term which has a number of distinct meanings. For Epicureans Otium was the quiet joy of an unassuming, contemplative, life. Thus otium is at odds with the Romantic idea that heroic struggle is something to be sought out.
Materialism – The belief that matter is the main constituent of the universe and that all phenomena are derived from the interactions of matter and the laws of the universe. Epicureanism is a materialist philosophy because it does not posit immaterial souls, or spirits, or gods made of divine stuff. Not to be confused with a love of material things.
Soul – When Epicureans refer to the soul they generally mean consciousness or mind. The Epicurean soul is composed of atoms and does not survive the destruction of the body.
Tetrapharmakos- A short summary in four parts of the beliefs of Epicurus recorded by the Roman Epicurean Philodemus.
Don't fear god,
Don't worry about death;
What is good is easy to get, and
What is terrible is easy to endure.
Mmm, that's some good surrealism!