My copy of Xenophon has a sentence that looks like this:
...because she alone makes the development of moral excellence [arête] a public duty.
(italics are in the quote itself; "she" refers to Sparta)
What does [arête] mean here? Online, I could only find information about a certain type of rock formation.
This addition in square brackets is not supposed to be part of the running text; it is a note to inform the reader that the term moral excellence was chosen by the translator to represent the Greek word ἀρετή. The purpose of such a note is to allow those who know some Greek to understand the possible nuances present in the Greek word that might be lost in translation. Arête is an (incorrect) translitteration of the Greek word into Latin letters (it should be aretê).
It could be argued that this question is about the practice of translators; as such, it is neither about the Greek word, nor about the meaning of an English word per se; but it is about an important aspect of the profession of translators, which is probably part of the curriculum of most students of English literature. As such, it might be considered on topic for this website.
On the other hand, the reading of texts written in English, such as this one, and the correct interpretation of conventions used in many English texts of the same genre, might be considered part of the English language and its usage, and hence also on topic.
P.S. The spelling error may be caused by confusion with the unrelated geographical term arête, which is originally French but also used in English.
As noted in the comments on your question, arête is a misspelling of arete, meaning “excellence of any kind”, particularly moral excellence (as used in your example). When transliterated directly from the Greek ἀρετή, it is also spelled aretê or areté. Thus, the circumflex is not an error, but is misplaced. In your example, arete is used only as a synonym for moral excellence.
