The noun ετος (etos) means year (Matthew 9:20, Luke 3:1, John 2:20). This word comes from the ancient Proto-Indo-European root "ut", meaning year. The adverb of time περυσι (perusi), meaning last year, also makes use of this ancient root, as do the Sanskrit word for year, vatsa, and the Hittite one: whitish. And since longer periods of time are commonly expressed in years, the Latin word veteranus, from whence comes the English "veteran", makes use of the same root.

Our noun ετος (etos) is used 49 times in the New Testament, see full concordance, and also occurs in the New Testament as part of the following compounds:

The curious noun ενιαυτος (eniautos) also means year, or more precise: anniversary (a word that comes from the Latin word for year, namely annus, plus the verb verto, to turn or return). Our noun combines the common preposition εν (en), meaning in, at, on, with the familiar pronoun αυτος (autos), meaning self.

In the classics this noun is often used as synonym of ετος (etos), meaning year (see above), but because it doesn't actually speak of any particular length of time, merely the fact that we've gone full circle, it also became used to signify a return or completion of much greater cycles (up to 600 years). It is used 14 times in the New Testament; see full concordance.

Formally unrelated to the above but spelled the same, the adjective ετος (etos) or ετεος (eteos) means true or genuine. It's relatively uncommon in the classics. A much more common word for truth is αληθεια (aletheia), which occurs a whopping 110 times in the New Testament, against zero times for ετος (etos), but it's not immediately obvious how the two differ or even relate. If our adjective is Indo-European, it derives from a very poorly attested root of dubious meaning. There doesn't appear to be anything fitting in Hebrew that might have been its source.

However, the Hebrew word for year is שנה (shana), which follows from the verb שנה (shana), to change or create a difference usually by repetition. Verb שנן (shanan) means to sharpen: to stroke a blade repetitively against a stone, or a mind against some exercise. Verb שנה (shana) means to repeat. That means that in Hebrew, the word for year has to do with repetition and hence confirmation. That's not to say that the Greeks somehow copied this custom and began to use their own word for year to express confirmation, but rather that the core meaning of the Indo-European idea of a yearly cycle also expressed a kind of return, repetition or even confirmation, which may have caused the words for year and confirmation to converge.

As said, our adjective ετος (etos) does not occur independently in the New Testament, but from it derives the verb εταζω (etazo), to examine, try or test. This verb again is rather rare in the Classics and not occurring in the New Testament, but from it come the following: