Phantasia is the technical Stoic term for an impression — the mental presentation of something to the mind. The word is broader than English impression; it covers sensory perceptions, memories, imagined scenarios, and the propositional content of beliefs as they first arrive.
The Stoic epistemology distinguished several kinds of impression. The most important is the phantasia katalēptikē — the cataleptic or cognitive impression, the impression that grasps reality so clearly that it could not possibly be otherwise. This is the impression on which secure knowledge is based. By contrast, phantasia akatalēptikē — the non-cognitive impression — is one whose accuracy cannot be vouched for, and which the sage will refuse to assent to as if it were certain.
The ethical analogue is more important for practice. Each impression carries with it a proposition — this is dangerous, this is desirable, this is intolerable, that person is a fool — and the Stoic rational faculty's job is to examine the proposition before granting sunkatathesis (assent). Most psychological disturbance, on the Stoic theory, comes from automatic assent to impressions whose propositions are false. Prosochē is the discipline of catching impressions before they are granted that assent.
Epictetus uses the word constantly. The most famous formulation — it is not things that disturb us, but our impressions about things — is the paraphrase of Enchiridion 5, not the Discourses; the Discourses return to phantasiai repeatedly but never quite in that crisp form. The impression is the immediate proximate cause of distress, not the event itself. So the leverage is at the impression, not at the event.
A useful analogy. The impression is like a thought presenting itself as a fact. She thinks I'm a fool. That is not a fact; it is an impression carrying a proposition. The Stoic does not necessarily reject it (she may indeed think you are a fool) — but the Stoic refuses to grant automatic assent. He examines: is there evidence? Even if true, is the proposition load-bearing for anything I should be doing differently? The examination is the whole practice.