Heh. That’s not a simple question, because all the Offices shifted in time over the centuries, and then recently they got shifted and renamed AGAIN. Also, people used to move some of the Offices up in time, if there were time conflicts. Also, of course the day was longer during the summer and shorter during the winter.
But the general idea was that Vigils was during the depths of the night (which became called Matins because it was in the very very early morning or midnight, and later Matins became the bedtime office). Lauds was at dawn, midnight, or right after Matins, and called that because you sang the psalms of praise that started with “Laudate” (Praise). Prime was originally the first hour after sunrise, but ended up being sung at midnight lots of places. Terce was the third hour after sunrise (about 9 AM), but moved up to dawn. Sext was originally about noon, but moved up. Nones was originally at 3 PM, but eventually was said at noon. (That’s where the word “noon” came from.) Vespers was originally at sunset when they lit the oil lamps/candles, but moved up to anywhere between 4 and 6 PM. Compline (Completorium, completion) was originally at bedtime, but turned into sunset. Matins was at bedtime. (Also, a lot of these got smooshed together at various times.) Sorry this isn’t a very clear explanation.
Anyway, nowadays, they’ve tried to move all this back to the original times.
Anyway, the rationale behind all these times is the seven times a day when devout Jews would pray to God: at midnight, dawn, midmorning, midday, afternoon, sunset, and bedtime. (You probably knew that.)
The old online Catholic Encyclopedia covers all this more accurately and completely than I can. (It’s under the article “Divine Office”, and the separate articles for all the various Hours.)