Εσχατος (eschatos) is a Greek word that normally translates into English as last. Greek lexicons like Thayer and Vine translate it by various superlatives like last, uttermost and lowest. From ἐσχατος we get the English word eschatology which means study of the last times.
On the day of Pentecost, Peter quoted Joel with the words, “And it will be in the last days, says God, that I will pour out My Spirit on all flesh” (Acts 2:17).
This raises the question “when are the last days?” Were they back in AD 33? Or, as many people believe, are we living in them now? And if we’re living in them now, is the world soon going to end?
What did Joel actually say? “It shall come to pass afterward, that I will pour out my Spirit on all flesh…” (Joel 2:28).
Or, if you’re interested,
All 3 of these ancient languages simply have afterward or after this. No mention of later or last.
The Greek of Acts 2:17 is “και ἐσται ἐν ταις ἐσχαταις ἡμεραις (λεγει ὁ θεος) ἐκχεω ἀπο του πνευματος…” It clearly uses the word ἐσχατος.
So why did Peter use the word ἐσχατος when he quoted Joel?
Well, of course he didn’t use the word ἐσχατος because he was speaking in Hebrew not Greek, and no doubt he would have quoted Joel correctly. Luke, who wrote Acts, must have interviewed somebody who heard Peter’s speech and helped him translate it into Greek.
It looks to me as if ἐσχατος normally means last, but can also have the sense of later.
This link - Eschatos - Blue Letter Bible – gives all the NT verses that include the word ἐσχατος and later would make better sense than last in several of them.
New Testament times were certainly much later than Joel, but they were not the last times. Now is much later than New Testament times, but I don’t think we are in the last times - unless the world is about to end. There is still more time to come!
Later would make much better sense in Acts 2:17 and in many other New Testament references.