In 2004, Jack, Kate and Locke were chased into the caves by a swarm of bees. Inside, they found the remains of two bodies. Locke called them Adam and Eve. Jack, being a doctor, stated the bodies must have been dead 40-50 years based upon the deterioration of their clothing. Jack found black and white stones, but failed to tell Locke of his discovery.
In 2007, when Jack and Hurley went to the caves, Hurley thought that the skeletons might belong to two of the Flight 815 survivors as a result of time travel.
In the Jacob-MIB centric episode, "Across the Sea," we learn the identities of Adam and Eve: Jacob's brother and their crazy, adoptive mother. Jacob placed them in the cave after his brother killed Mother in a rage, and after Jacob threw his brother's body into the light cave, killing his mortal soul. From that point forward, Jacob used black and white stones to represent him and MIB.
For some, the revelation of the names of Adam and Eve was a non-event. It also showed that Jack's assessment of decomposition was off by thousands of years.
The cave of Adam and Eve was one of four burial rituals shown during LOST. The concept of laying out bodies in caves as a funeral rite goes back thousands of years in the Middle East. But it begs the question, how did Jacob know of that custom if he was born on the Island and separated from the Others?
The other known grave was the pit where Ben had the Others toss the purged Dharma members.
This mass grave is representative of warfare.
For the Others, we saw Colleen's ritual to be a Viking-style funeral pyre. It was apparently done to avoid that person's body being taken by MIB. The crash survivors used cremation of the deceased passengers from the plane in a beach funeral pyre.
Afterward, the 815ers buried their dead in a graveyard. The Tailies also did the same during their separation from the 815ers.
Who were Adam and Eve? Jacob's brother and his adoptive crazy Mother.
Why were they buried in the cave? Jacob did it out of respect and/or grief.
What role did Adam and Eve play in the resolution of the LOST story? A footnote in Jacob's back story.