I would be cautious about making strong generalizations about what a polysemous word like kairos meant, for context and usage were as always the main determinants of meaning. The later liturgical use of kairos to refer to "God's time of acting" (mentioned in the Wikipedia article) represents a later specialized sense and it would be misleading and anachronistic to read that back into the NT. One helpful point is to recognize that in ancient Greek there were at least two words used to refer to "time", kairos and khronos, and that the range of meaning in one was not identical to the other. Time was viewed in at least two different ways by ancient peoples. The more pervasive understanding emphasized the experience of time as an unceasing succession of regularly occurring events, of "times of planting and harvest, cold and heat, summer and winter, day and night" as Genesis 8:22 puts it. The famous discourse in Ecclesiastes 3 is perhaps the most sublime expression of this view towards time, in which the very rhythm of time follows cyclic and alternating events. The other view of time is that it is a fixed linear progression of chronological time-units of equal length, as measured by a chronometer or a clock. Events may occur within this stream of time but they do not set its rhythm. There is a natural overlap here because months, days, seasons, and years are both cyclic "times" as well as indicators of chronological time. Hellenistic Greece, which developed fairly sophisticated technological devices for measuring time, viewed time more often from this more modern perspective.
Now, some reference works would say that the more traditional view of time was indicated by kairos and the second was indicated by khronos. That's true to some extent, but the meanings overlap mutually. Thus, the translators of the LXX often used khronos to render various Hebrew expressions that viewed time in terms of events. A good example is Esther 2:15 LXX in which the clause "when Esther's turn (khronon) came" clearly uses khronos in a non-chronological sense. A more relevant distinction between kairos and khronos pertains to the duration of time. Millar Burrows (JBL, 1955) noted that biblical Hebrew "does not speak of fulfilling time, but of fulfilling days or years. The Hebrew words for 'time' indicate ordinarily a point rather than an extended period of time" (p. 4). The Greek of the LXX is influenced by the Hebrew, and the NT is influenced by the LXX in turn. So what is interesting is that kairos more often indicates a point in time, while khronos more often refers to a duration like "days" or "years" (which, btw, are also counted and reckoned chronologically). Consider these examples pertaining to the same type of event, the birth of a child:
"And the days (hai hémerai) for her [Rebekah] to give birth were fulfilled (epléróthésan) and thus there were twins in her belly and the first-born came forth entirely red and with hairy skin. And she named him Esau" (Genesis 25:24-25 LXX).
"And it came to pass in the time of the days (tó kairó tón hémerón) that Hannah bore a son and she called his name Samuel" (1 Samuel 1:20 LXX).
"The woman became pregnant and she gave birth to a son next year at the same time (ton kairon touton) that Elisha had foretold (2 Kings 4:17 LXX)
"Do you know the time (kairon) when the mountain goats give birth and do you watch the doe's birth pangs? Do you count the months (érithménas ménas) until the pregnancy is completed (pléreis) and can you set forth their birth pangs?" (Job 39:1-2 LXX).
"And Elizabeth fulfilled (eplésthé) the time (ho khronos) of her giving birth and she bore a son" (Luke 1:57).
"And it came to pass while they were there that the days (hai hémerai) for her [Mary] to give birth were fulfilled (epléróthésan), and she gave birth to her son, a first-born" (Luke 2:6-7).
What is interesting is that khronos, kairos, and hémerai are all used to refer to the same overall event but khronos is used like hémerai "days" to refer to a duration that is "fulfilled" or "completed" by the punctual event of "giving birth", a duration which consists of countable "months", whereas kairos is used to refer to the moment of "giving birth" that terminates or fulfills the period of pregnancy. And so in the NT, the idea is often that one must keep track of the khronos in order to know when the kairos comes. The "time" (kairos) for a scheduled event like the departure of a ship would be reckoned by counting the "hours" or "days" or whatever. But the kairos does not necessarily have to be reckoned; many events, especially unexpected ones or those appointed by God, cannot be chronologically reckoned.
This seems to be the point in the eschatological material in the synoptic gospels. Matthew 13:30 refers the future Judgment Day as the "time (kairó) of the harvest," using the familiar OT term to refer to such cyclic events, and yet this is not an event that can be fixed chronologically for the exact number of "days" and "hours" are not known (24:36), and these are the time-units by which chronological time is measured. So for those who think they know the "time" of the Son of Man's approach will claim that he is "delaying" (khronizei, "passing time" in 24:48, 25:5), i.e. he comes "after a long time (meta khronon polun)" in 25:19, the "length" of the time being judged by such things as days and hours. Compare Luke 19:44, with respect to the coming judgment on Jerusalem: "You did not know the time (kairon) of your visitation". The use of kairos in Luke 21:8 has the same sense to me, saying that the kairos "has approached" means that one claims to know when it it supposed to come. But while the mention of "days" and "hours" lends itself to reckoning time through its measurement, the example of the fig tree in 21:29-31 clearly shows that time is also being reckoned non-chronologically through the observation of the changes of the seasons (i.e. "signs"). This concern is paramount because the disciples had asked for a "sign" in the narrative context. So in both texts, time seems to be viewed from both perspectives.
Moreover when kairos is not viewed as an end-point of a duration (like pregnancy or the eschatological harvest at the "end of this world" in 24:3), the event it indicates can naturally also have a length such as a season, and punctuality can also be indicated by modifying khronos (such as stigmé khronou "moment in time" in Luke 4:5). Daniel was an especially influential book for NT eschatology and kairos occurs in the LXX to render the Aramaic ydn, which -- unlike kairos elsewhere in the OT -- is numerically reckoned as "years" (cf. 4:13, 20, 22, 29, 7:25), e.g. the "3 1/2 times" of 7:25 corresponds to the "half-week" of ch. 9; cf. the quotation of 7:25 and its interpretation in Revelation 11:2-3, 12:14. H. Louis Ginsberg has pointed out that this use of "time" to mean "year" reflects the Greek use of khronos to mean the same thing. And so in passages in the NT influenced by Daniel, kairos can have a similar sense as khronos such as in Luke 21:24 which refers to Jerusalem being trampled by the Gentiles (cf. Daniel 7:23-25, 9:24-27) "until the times (kairoi) of the Gentiles are fulfilled (pléróthósi). Here kairoi is a duration being "fulfilled" like the khronos of Luke 1:57 or the hémerai of Genesis 25:24-25 or Luke 2:6-7. This reflects the idiosyncratic fact that while Hebrew does not speak of "fulfilling time," the Aramaic of Daniel does speak of a duration of "times" that are fulfilled, and the choice of the translator to use kairoi here ...and so Luke uses the term kairoi in a way that differs from the other cases. This just shows how fluid and complex the use of such terms were.