Drawn to this mysterious, desolate world, the Doctor, Barbara, Vicki, and Ian (the latter two lend their voices to this dramatization) discover beautiful crystalline statues and are attacked by a savage black fog. To their horror and curiousity, the discover that both of these things are very much alive. One is a race of light-based energy beings who can resonate their bodies into crystalline forms, the other is a race of darkness-based energy beings sharing a single consciousness. Each wants the other dead, and each is developing their own strategies for how to accomplish that goal while sustaining their own existence after the dying star finally burns itself out.
Dialectic conflicts were an understandable topic of dissection in the Sixties, considering that this was the height of the Cold War and the Civil Rights Movement. Televised Science Fiction enjoyed a brisk trade in crude allegories for such things. Consider the Federation and the Klingons in the original Star Trek, or the particular episode Let That Be Your Last Battlefield in which the two final survivors of a war-torn world are keen to see each other to the grave, for no other crime that being half-black and half-white but on opposite sides of the body.
The Dark Planet takes this dialectic theme to its most precise analogy: one side is literally Light and the other side is literally Dark. Their existence is tied to each other and they have the knowledge to help each other survive if they would only put down arms (so to speak). And in Doctor Who nothing is as simple as the Light side being morally good and pure, nor the Dark side being irredeemably evil. Can the Doctor reconcile these two sides and restore their sun?