Maya and Aztecs were roughly neighbours, though the Maya were descended from ancient Mesoamerican people in that area, while the ancestors of the Aztecs (at least the ruling dynasties) were thought to come from the north in the last millennium.
The Maya civilisation grew up from small Maya-speaking tribes in the southern Guatemalan and Mexican hills, who developed sophisticated mathematics, calendars, architecture and writing. they formed a number of powerful city states, though not an empire. For some reasons, not yet understood, their southern civilisation collapsed in a short period, the cities being abandoned. However, further north smaller Maya towns began to flourish. The focus of their civilisation moved to the centre and north of the Yucatan peninsula. They were still flourishing economically, though with lesser architecture, at the time of the Spanish conquests.
The Aztecs seem to be a result of a dynasty of warlords from the northern areas (possibly the Mojave area) who dominated a central Mexican area. Due to a lack of land, they built settlements in a lake, and this later grew into the metropolis of Tenochtitlan. They became militarily powerful, and began to carve out a large empire, encompassing much of central Mexico. They were feared and loathed by their enemies, infamous for their bloodthirsty rituals of massed human sacrifice. They were still in the ascendant when the Spanish arrived.
The Incas were a very different people living thousands of miles away in the highlands of the central Andes. They inhabited a town (Cuzco) in a valley, along an increasingly important trade route. Their wealth allowed them to spend on a large army and they set about expanding. They became dominant in much of the central Andes, and even conquered the rich coastal trading cities like Chan-chan. They established a network of roads and administrative centres, famously including Machu Picchu. They suffered a devastating civil war just before the arrival of the Spanish, and only succumbed to the new conquerors.
