If I get some time tomorrow I'll try and type out a full answer and provide some secondary sources, though for now I can offer a bitesize answer.

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Typically morbid curiosity topics like these end up being overstated in pop culture, but you'll be glad, or perhaps horrified, to know that the Aztecs (and other pre-Columbian civilisations) live up to their sacrificial reputation.

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Sources are a little patchy for the period, but through corroborating several accounts we can begin to paint a fairly accurate picture. Bernal Diaz, one of Cortes' fellow conquistadors wrote a fantastic book in his later years called Historia verdadera de la conquista de la Nueva España (The True History of the Conquest of New Spain), which when combined with information from the Aztec codexs, the accounts of Bartolomé de las Casas, and archaeological evidence, can be considered broadly accurate.

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Diaz notes that in every town or city they stopped at in their various expeditions through Mexico, there was plenty of evidence of human sacrifice, from bloodstained temples to racks of human skulls known as tzompantli. Upon reaching the Aztec 'capital' Tenochtitlan, the conquistadors reportedly found a literal pyramid of human skulls; cortes ordered two soldiers to count them and I believe their estimates were somewhere around 10 000.

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There are a lot of theories on why the Aztec's practiced human sacrifice, and in reality there were probably several reasons for it. Namely was appeasing a central diety, Huitzilopochtli, who among other things was considered responsible for the rising of the sun. Archeological (and some written evidence) confirms that sacrfices indeed took place at the Templo Mayor, the main temple of the city constructed as a dedication to Huitzilopochtli.

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In a practical sense, sacrifices also satisfied two needs for the Aztecs. One is the obvious motive of invoking fear in their enemies and neighbours, necessary to ensure the political hegemony of Tenochtitlan and obidence of their tributary states. Another (debated) reason, relates to Aztec war practice. It was seen as a great honour and a sign of a true warrior to capture your opponents rather than kill them on the battlefield. These prisoners would obviously require feeding however, and frequently the Aztecs experienced troubles with food supply and sustenance, partly due to a failure to domesticate any large mammals. Sacrificing their prisoners therefore removed any food burden they created.

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Finally one thing to note. Occasionally you hear arguments that captives were sacrificed to appease the Aztec's alleged cannibalistic diet. Whilst it is likely ritual cannibalism was practiced to some degree, human flesh was not a staple of the Aztec diet and there's no sources or logical reasons to believe it was, despite the claims of a few maverick historians. More on this can be found in two great articles - George Pierre Castile's 'Purple People Eaters?: A Comment on Aztec Elite Class Cannibalism' and Stanley Garn's wonderfully titled 'The Non-economic Nature of Eating People'.

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There's always room for discussion, but perhaps the section Human Sacrifice and Blood Sacrifice from our FAQ will answer your inquiry.

Thank you for the detailed answers!

I've never heard of the archaeological evidences for human sacrifices, which sounds quite intriguing. I came upon this recent article which reports discovery of the skull racks in Mexico City. https://www.sciencemag.org/news/2018/06/feeding-gods-hundreds-skulls-reveal-massive-scale-human-sacrifice-aztec-capital

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I have another question about the capturing of enemy warriors in combat: do we have any evidence of how exactly this was done? I would imagine grappling and subduing an armed opponent would be a very difficult thing to do, and trying to restrain him with a rope would completely expose you to other enemy's attack. Did the Aztec warriors operate in team so others would be able to provide cover while another restrained the enemy? Or did they have some sort of established rules with the neighboring states for surrendering and capturing in battle?