Barbara has an interesting reaction to the setting. The Aztecs had many aspects to their civilization, a high degree of learning, awareness of astronomy etc, but they also performed human sacrifice. Barbara has a specialty in Aztec civilization (she's a teacher) and wanted to take the opportunity of being a God to attempt to sway the Aztec civilization to end their practice of human sacrifice.
Another thread of the story is marraige-making. The Doctor took a liking to a lady in the gardens, and ended up engaged to marry her.
All the times I've seen this I can't shake how unauthentic the weapons looked. The sets and clothes and settings, they look like they came straight from the paintings of Aztec buildings etc. But the weapons look completely wrong, but maybe it's the goofy ass fighting style. In any case it's clear they wanted this to be a serious portrayal of Aztec civilization but there are things like the goofy looking "weapons" which detract from this for me.
The most key point perhaps is the Doctors insistence that they cannot change history. The Doctor tells Barbara "You can't rewrite history! Not one line!" Yet, isn't that what Time Lords do, modify lines of history? But at times throughout Doctor Who it's been asserted some pieces of history cannot be changed. An example is in the modern Father's Day episode where the Doctor and Rose rewrite Rose's history, and that little bit of modification causes all you-know-what to break loose.
This is a question which runs through many science fiction works and is a speculation of scientists. But as we do not have good knowledge of the operation of Time, we cannot tell whether "You can't rewrite history! Not one line!" is actually accurate, or not.