They were a newer tribe who migrated down fr the north. The Aztecs overthrew the former lords of the region, the Toltecs, whose capital was at Teotihuacan (IIRC). Thereafter they applied pressure in all directions and expanded, usually subjugating neighbouring cities and tribes, and thereafter demanding tribute fr them (human sacrifices).
The Aztec military campaigns could be described as a sort of religious practise in which the army invaded other places and took back prisoners for the human sacrificial rites they practised. Seniority in the army (and status) for each individual warrior depended on how many captives they had taken.
The Aztecs were still expanding rapidly when the Spaniards arrived. Thereafter, the Spanish allied with all the disaffected tributary tribes (there were many cos of the human sacrifice thing) and defeated them. Or something like that.