Somewhere on Earth, in a small cave, I found a strange dark object on the ground. When I approached the thing, it said "Disturb the Remains." After I pressed it (and waited couple of seconds), it started playing a very strange audio (I was unable to understand it). What is the point of this, and what exactly is it saying?
That spot where you find the cave was the original location of the infamous Loot Cave, a cave that would spawn endless amounts of enemies and allow you to grind for exp and drops. After that was removed by Bungie in a mandatory update, another Loot Cave was added elsewhere.
You're probably referring to this spot:
The spot where you see the prompt to "disturb the remains" is merely an easter egg that refers to, at least according to this source, "A reference to the Cryptarch present on the game’s Tower, and the man who sells or decodes the many Engrams players farmed in the now-defunct spawn point."