A criterion is one standard you measure something against when you are judging it. Price is one criterion when you are choosing a flat; the walk to the station is another. A job advert that lists what a candidate must have is listing criteria.
The plural is the thing to get right: one criterion, two criteria. A criteria is wrong and criterias does not exist, because English borrowed the Greek pattern along with the word, the same pattern as phenomenon and phenomena. Criteria takes a plural verb: the criteria are strict, not the criteria is strict. The word lives in formal writing — marking schemes, funding applications, medical guidelines, tender documents — while in conversation people say standard, requirement, or what we're looking for. You set criteria, you meet criteria, and a patient meets the criteria for a diagnosis.
1nouncriterionA standard or rule by which something is judged, measured or decided.
“Cost was the only criterion that mattered to the committee.”
criterion is a standard.
Criterion came into English through New Latin from Ancient Greek kritērion, a test or a means of judging, built on kritēs, a judge, and krinō, to judge. The same Greek family gives critic, critical and criticism, so a criterion is the measuring stick the critic is holding. The odd plural is Greek grammar that rode into English on the back of the word and never got off.
Proto-Indo-European
*krey-
Ancient Greek
κριτήριον — a test, a means of judging
New Latin
criterion
English, today
criterion
Built from
From New Latin criterion, from Ancient Greek κριτήριον (“a test, a means of judging”), from κριτής (“judge”), from κρίνω (“to judge”); see critic.
Etymology from Wiktionary, CC BY-SA