This is not an historical question, but rather an anthropological. Human burial practice goes back tens of thousands of years, well into the middle paleolithic period, and possibly as far back as 100,000 years link.

The significance of human (I should say hominin, really) burial is multi-faceted. First, burial of a corpse could indicate "care" for the deceased, as burial prevents (or hides away from the living) the processes of decomposition. It also protects the corpse from overland scavengers like vultures. Protection of a corpse is one of the easiest and earliest signs of a certain cognizance of life and death, of reverence for individuals. In the Bronze Age, corpses become associated with pollution, especially ritual pollution, and we can see signs of this in even earlier epochs. We typically see burials grouped together, often in vast fields (as today), and usually (but not always) removed at a distance from the dwellings of the living. In fact, the vast majority of physical evidence of paleolithic cultures comes from burials.

Ideas about the corpse going on a journey to some kind of afterlife are also prevalent. Even the Qafzeh burials, at the extreme early end of the scale, show clear signs that the bodies were "prepared" for a next stage of life (err, un-life). Egyptian grave goods are well-known--the possessions of the deceased to be utilized in the world after death. Burial as a preparation for a next step is a very common, nearly universal concept in hominids. Even Neanderthals show signs of this behavior (though some argue that Neanderthal burial is slightly different in intent).

At its most basic, though, I think the cultural anthropologists have it right: burial is a basic cluster of behaviors that not only seeks to honor the departed, or at least mark out that they have passed, but also remove the corpse and the memories associated with the corpse, good or bad. It is a coping mechanism for unhappy feelings, which were identical to ours back then as now. Very few other animals show real signs of mourning or understanding of death (great apes for sure, and also dolphins and canines I believe?). Earliest attempts perhaps just moved the corpse into a nearby woods, but then parts of the body showed up because wolves had torn it apart. Putting the corpse in the ground is the most expedient way of removing the corpse from the world of the living permanently. All the later developments (grave goods; inhumation vs cremation; tomb-building; grave fields; death ritual; etc) probably stem from this initial instinctual behavior.

In 2013, hominin remains were discovered in the Rising Star Cave system in South Africa. Subsequent excavation revealed a number of nearly complete skeletons of the new homo naledi, about 300-250 thousands years ago. These remains were deposited over time, in successive clay layers, and no other types of bones were found. There is no evidence that water washed these bones into the cave, which is very hard to reach, and no evidence of predation (ie that some apex predator killed the hominids and drug them to its lair). The implication is that we are seeing strong evidence of burial behavior. A lot has been written on this topic since then. Any search for "Rising Star Cave" or "homo naledi burial" will bring up interesting discussions, or head over to /r/AskAnthropology for more.