Why did they do it? How did these ideas fit with their social organization?

I'm going to cherry-pick this question. You have asked something that is impossibly huge to answer here. Even an entire dissertation (ahem) is not sufficient. At first I was going to skip this, but you've got a good question here that I can at least make a stab at answering. I'm going to focus on just one little corner of the Mediterranean in one time period: Iron Age ("Dark Age") Greece, 1000-700 BCE. I'm going to cut and paste some from class notes, because I'm a little lazy.

We start at a place called Lefkandi, on the Greek island of Euboea. There, a little after 1000 BCE, a "big man" was enjoying some relative success at being something like an aristocrat. It was the world after the Mycenaean collapse, and things had been bad for a while all over Greece: the entire system of how things had been was disrupted. Imagine Mad Max, but without vehicles and much less fun. Anyway, this guy at Lefkandi had made himself into a pretty big deal. When he died, his relatives(?) buried him in a way that was unprecedented. First, they built a gigantic structure (45 meters long!). The size of the structure earns it a place among a very short list of buildings in this early period which can be termed “monumental” and is often cited as evidence of a level of community organization distinctly lacking in the other major settlement centers of post-Mycenaean Greece. Inside it, in a shaft, the man himself was buried. His ashes were gathered in linen and placed in an heirloom bronze amphora from the 12th century. With it was a whetstone, an iron spear head, an iron razor, and an iron sword blade. Next to him was a female, inhumed instead of cremated, and with her was a collection of bronze and iron pins, a gold and faience necklace, gold and electrum rings, gold hair spirals, in ivory-handled knife, and two golden discs above her breasts. In a shaft next to them, the skeletons of four horses were found -- sacrificed during the burial. Then, apparently, the whole structure was covered over to make a very large mound (there is some controversy about this part).

What was done at Lefkandi in the real world is very similar to what we hear about in Homer, in the "Heroic Age" of imagination. Most believe that Homer's epics, dating to the end of the 8th century, contain the echoes of memory stretching back into the "Dark Age" society of centuries earlier. If so, we have one such case here. Listen to how the poet describes the burial of Patroclos:

...and on the pyre he set vessels of honey and oil, leaning them against the bier; and four horses with arched necks he swiftly cast onto the pyre, groaning greatly. Nine dogs had feasted beneath the table of [Patroclos], and Achilles, cutting the throats of two of them, threw them atop the pyre, and in addition twelve great sons of the Trojans he slew with bronze blade; he had grim deeds in his heart, and to the pyre he set the iron might of fire, that it might consume all. (Iliad 23.170-77)

Later, when Achilles dies, we get a description of his funeral:

But when we had carried you from the battle to the ships, we placed you on the bier, cleansing your comely flesh with warm water and anointing oil; and many warm tears did the Danaans shed around you and they cut their hair in grief. From the Sea your mother came along with the immortal sea-nymphs when she heard the news. A divinely-resounding cry arose over the sea [...] thus for seventeen days and nights alike, we mortal men and immortal gods lamented; on the eighteenth day we gave you to the fire, and around you we slew many very fat sheep and twisting-horned cattle. You were burned in the clothing of the gods and in an abundance of oils and sweet honey; and the multitude of Achaean heroes were moving about the pyre in their armor while you burned, infantry and horsemen alike, and a great din arose. But when the flame of Hephaistos consumed you, that morning we gathered your white bones, Achilles, in unmixed wine and oil; your mother had given a golden, two-handled urn, saying it was the gift of Dionysos and the work of renowned Hephaistos , and in this lie your white bones. (Odyssey 24.43-76)

Many of the elements at Lefkandi are here: the sacrificed horses (and possibly the woman was "sacrificed" at the time of the big man's burial; that's a topic for another thread). We have the mound and the cloth and the nice urn for the ashes.

(con't)