After fleeing Marinus and its Science Fictional analysis of the subject of freedom and free will, the TARDIS materializes inside an Aztec tomb of the 15th century. This is readily identified by Barbara, the history teacher for whom the Aztecs were a particular field of interest. To her, the era of Tenochtitlan was a fascinating and romantic time, an intriguing and tragic period where the greatness of civilization mingled with the most gruesome horrors. She always wondered if they could have been spared destruction by the Spanish Conquistadors had they been able to excise the evil of human sacrifice from their midst, and when she emerges from the tomb and is mistaken for a reincarnation of the ancient priestess/goddess Yetaxa, she is given the chance to put her once idle speculation into practice.
If you could go back in time and kill Hitler, would you? Or could you? The Doctor admonishes Barbara, telling her... yelling at her... that she cannot change even one line of history. Yet whether he was talking about a hard and fast rule of temporal physics or a moral imperative handed down from the Time Lords themselves, there is a deeper matter to consider. As demonstrated amusingly by Desmond Warzel's short story Wikihistory, everything in a society is linked in an "ecocultural" web with everything else. To tug at one string risks unravelling everything, so deeply intertwined as they are. Killing Hitler prevents the German missile program, which in turn stalls the American aerospace initiative, computers, the Internet and time travel itself.
A do-gooder from the future must also contend with the zeitgeist of the time they travel to. Simply killing Hitler would do nothing to alleviate the unrest in Germany that facilitated his rise to power. The spark would be rid, not the tinder, not the hot coals. Ian reminds Barbara of this when they debate their course of action with the two high priests of the Aztecs.
On the one hand is Autloc, the high priest of knowledge and embodiment of every civilized, high-minded and noble enterprise of the ancient Mexican peoples. On the other is Tlotoxl, the "local butcher", high priest of sacrifice and walking stereotype of the bloodthirsty, scheming and barbarous. Curiously, and the most nuanced aspect of what is otherwise a fairly crude dialectic, it is the enlightened priest that entertains the idea that Barbara truly is the visitation of Yetaxa. Tlotoxl has no use for her once she begins meddling in his religious duties. He would challenge the gods themselves if they interrupted his duty.
Barbara sees the problem as a simple matter of trying to convince the Aztecs through Autloc that human sacrifice is unnecessary. The rains will come without shed blood, the sun will reemerge from an eclipse without spent life, and Autloc knows this. Ian, however, exclaims that he is the rarity in Aztec society. She acts as though the people are simply waiting for the word of wisdom to come from on high, only to be reminded by her pragmatic companion that, in reality, they are far more in line with Tlotoxl's way of thinking. It isn't just the single agent in a society that needs to be removed, a single practice. The whole society is a unit, a tangled web.