The Core is a very mysterious thing in Cave Story.
Many here speculate that The Core serves to counteract Ballos' presence in order to keep the island afloat. This consensus is best described in the words of Misery in Carrotlord's mod, A Lost Land:
Misery said:
Ballos could not kill himself, and he hated this fact. He subconsciously wanted the island to fall, so that the collapse would crush his body. Even that wouldn't kill him, though he kept trying. We needed the Core to counteract the presence of Ballos. But without him, the island is able to float naturally.
But then making this assumption begs the question: Did Jenka create the Core when she confined Ballos to the island? Or was the Core already in existence and she was somehow able to apply its power to her own use?
How is the Core connected to the Red flowers? According to Kazuma, it's because of the Core that red flowers make Mimigas go rabbid. And when the Core was destroyed, Sue who was infected by the red crystal was restored to her natural self. So many unanswered mysteries in this game...
So, after thinking this over, I've come to two possible conclusions:
1) The Core is a giant brussel sprout
2) The Core is a giant cabbage