Abarim Publications' online Biblical Greek Dictionary
The important noun ημερα (emera) means day, and survives in modern English in such useful words as hemeralopia (day blindness), hemerobaptist, (someone from a Jewish sect which practiced daily ritual bathing) and hemerocallis (a lily that flowers for one mere day).
Where our word comes from isn't immediately clear but the word ημι (hemi), meaning half (hence our word hemisphere) certainly jumps to mind, specifically when we remember Jesus saying that there are twelve hours in a day (John 11:9), which is obviously half of the twenty-four we moderns are used to. That's because, unlike our English word "day", the Greek word ημερα (emera) is solely reserved for the lit half of earth's solar day, and particularly the goings on of a day (Matthew 6:34, Luke 1:23, Romans 14:5). Our word ημερα (emera) is often used juxtaposed to νυξ (nux), meaning night, or the period without legitimate activity (hence our word nocturnal; Matthew 4:2), and the two are creatively combined into the word νυχθημερον (nuchthemeron), or "night 'n-day", which covers the whole twenty-four hour cycle (see below).
Rather than exclusively denoting a stretch of clock-time of fixed length, our word ημερα (emera) may in a poetic sense denote any continual period during which legitimate activity is performed without interruption. As such our word ημερα (emera) means "uninterrupted procedure" or "routine" and may be used synonymously with "trial/hearing/test" (Acts 17:31, 1 Corinthians 4:3, 3:13). Hence Jesus submitted that he had been in the temple daily, or the whole time, while the evil of darkness continued nightly, also the whole time (Luke 22:53).
On the "the day of John's public appearance to Israel" (Luke 1:80), John may have showed up first but his initial showing up was the beginning of continued public activity. The "day of slaughter" (James 5:5), likewise, may not be associated with one particular calendar day and will probably also not last precisely twelve hours, but denotes an indefinite period of uninterrupted carnage. The same goes for the "day of judgment" (Matthew 10:5), the "day of redemption" (Ephesians 4:30), the "day of wrath and revelation" (Romans 2:5), and the "day of the Lord" (Matthew 7:22, Luke 17:24, Acts 2:20, 2 Peter 3:12). Likewise the "last day", upon which all mankind resurrects, is probably not a calendar day after which the earth stops spinning, but the final procedure before the new creation can commence (John 6:39-40).
Unlike our modern calendar, the Jewish one only had one week day with a name, namely the Sabbath, and the other days were numbered. Because the word for day really only means "uninterrupted period of activity", a section of a day is still a day. That may render a somewhat frustrating endeavor the puzzle of how long precisely folks were where (as some commentators appear keen to do), but here's a hint: Although Jesus was in the grave three days, he wasn't in there 72 hours. The only whole day he spent in the grave was the Sabbath; he went in on the day before and came out on the day after. That's three days (and the same goes for Jonah; Matthew 12:40).
Our noun ημερα (emera) is used 389 times in the New Testament, see full concordance, and comes with a small array of derivations and compounds:
- Together with the preposition επι (epi), meaning on or upon: the adjective εφημερος (ephemeros), meaning for the day. In the Bible this word denotes belonging to the daytime, but is really an equivalent of pertaining to routine activities (James 2:15 only). This and the next word survive in English, as ephemeral and ephemera, with the meaning of daily in the sense of not lasting any longer than a day: fleeting or transitory.
- Together with the preposition κατα (kata), meaning down from, down upon: the adjective καθημερινος (kathemerinos), also meaning daily or rather routine (Acts 6:1 only). Due to the similarity of the prefixes, this word and the previous two pretty much denote the same thing.
- Together with the adjective μεσος (mesos), meaning middle: the noun μεσημβρια (mesembria), literally meaning mid-day but with a surprising twist. This word occurs only twice in the New Testament. In Acts 22:6 it describes the time of day at which Paul famously met Jesus on the road to Damascus: at mid-day. In Acts 8:26 this word appears again in combination with a road, the one from Jerusalem to Gaza, upon which Philip met the official of Candace. Perhaps the angel told Philip to meet the man at mid-day, but perhaps he told him to head south, as our word μεσημβρια (mesembria) appears to have been used in the classics as a navigational term. How the word for mid-day came to denote the south is not wholly clear, but most likely because the sun rises both when it travels toward mid-day, and when an observer travels toward the south (in the northern hemisphere, of course).
- Together with the noun νυξ (nux), meaning night: the noun νυχθημερον (nuchthemeron), or night-and-day; a full day. English doesn't have a word for this but some other languages do. In Dutch this word translates as etmaal. In the New Testament this word occurs only in 2 Corinthians 11:25, where Paul submits that his ship went down during some point in the night and he wasn't fished out until some point of the following daytime.
- Together with numeral οκτω (okto): the adjective οκταημερος (oktaemeros), meaning of eight-days. This word occurs only in Philippians 3:5 where Paul uses it to describe a quality of him, pertaining to circumcision. It obviously literally means that he was properly circumcised when he was eight days old, but this word has all the fixings of being a colloquial buddy term; something like "good fella" or "home boy".