Doctor Who has a few iconic elements that remain with the series no matter what. You have, very very obviously, the Doctor himself, and his TARDIS looking like a police box even though she is supposed to have a chameleon function. And then you have Daleks. Oh, Daleks. There is something about angry shrieking murderous pepperpots that people just love. And this is the serial that first introduces the omnicidal maniacs and kicked off a worldwide obsession and a very silly Christmas song.
After the events of An Unearthly Child, the Doctor, Susan, Ian, and Barbara arrive in a petrified jungle. The Doctor is extremely interested in a city on the edge of the jungle and claims a fluid link is running low on mercury as an excuse to explore. However, they start getting lost, and Barbara is confronted by an oversized salt shaker that brandishes a plunger at her.
These are the Daleks, the cyborg inhabitants of the city that live off the irradiated atmosphere, which is sickening the others. They have been at war with the other inhabitants of the planet, the Thals. Susan is sent to collect some medicine for the radiation poisoning and deliver a message to the Thals, supposedly to suggest a truce. Of course, being Daleks, this is like believing the Nazis were inviting the Jews to a resort and spa instead of death camps.
This helped cement some key elements of the show. It shows the Doctor isn’t entirely amoral; he is horrified at the idea of the Daleks committing genocide. It also once again showcases that Susan wasn’t always utterly useless. She treks through the jungle while suffering radiation sickness just to help her friends. It also showed the Doctor’s insatiable curiosity, which gets him in trouble over and over and over again.
The serial also establishes the Dalek backstory, although it is revised a bit later on. The Dals and Thals were two warring races: initially the Dals (later known as the Kaleds) were scientists and philosophers while the Thals were a warlike race bent on conquest. One chemical and nuclear war later, the Dals have mutated into blobby tentacle thingies and the Thals were so horrified by their past that they have become pacifists. (They get better.) It also set the stage for the constant conflict between the Doctor and the Daleks: after all, if the Doctor had not told the Daleks he was from a different planet, they wouldn’t have realized there were other planets full of non-Dalek life that clearly needed to be exterminated.
This is more or less known as the serial that really placed Doctor Who firmly in the public eye and part of British culture.
"Don't worry, Susan, it's only a plunger." "IT IS NOT A PLUNGER." "Hmm, yes, definitely a plung--" "IT IS NOT A PLUNGER!!!"