The Edge of Destruction is what the Star Trek writers call a bottle story, as in a ship in a bottle--the entire story takes place inside the ship, so there is no need to spend money on new sets. The original title, in fact, was "Inside the Spaceship" and it was short--only two half-hour episodes. In it, the TARDIS appears to be controlled by an outside force. Could another intelligence have gotten into the ship?
After a small explosion, the time-travellers are rendered unconscious and awaken to find everyone acting strangely. They suffer from headaches, partial amnesia, and feelings of paranoid suspicion. Susan threatens Ian and Barbara with a pair of scissors, and they accuse each other of over-acting--sorry, I mean sabotage. And they discover that the TARDIS is racing backwards in time toward the Big Bang and total annihilation.
One thinks of haunted house stories or the many science-fiction tales in which the characters eye each other with suspicion, wondering if one or more of them are not what they seem. The story was well-received by the viewers, probably because of the character-revealing conflict. We also get to see more of the TARDIS. The actors appreciated it because what had been just a collection of four strangers became, at the end, a family group, and Whovians like to point out that the TARDIS appeared to be trying to communicate with its passengers, to warn them what was happening. It was many years before we began to understand just how intelligent she was.
The fact is: no one was sure Doctor Who would last and in case it was cancelled after a few weeks, they needed a quick two-episode filler to round out their short-term contract. It followed a long story in which the budget had been blown on Dalek construction.
Part 1
Part 2