mipsmam gave a pretty thorough answer on the linguistic and historical meanings of the word.
In purely political usage, Aztlán is sometimes used to refer to areas that were once Mexican territory in the Southwest. In the 1960’s, some Chicano activists, who resented their treatment as “foreigners” or “outsiders” in American society, embraced Aztlán as an ancestral homeland of the Mexica people - and placed this homeland within the Southwest, to legitimise their presence within this region.
Actually, the fact that these lands were Spanish for 300 years and then Mexican for another 30 or so years could have been used to make this point. But many Chicanos made a point to embrace their native roots and reject their (by their view imposed) Spanish or “Hispanic” identity. So instead of using Spanish land grants they used a Native American based source for this.
Since the 1960’s a handful of activists have gone further, expousing self determination and even independence for ‘Aztlán’. However these views are definitely not widely held. The one professor that became identified the most with this, Carlos Truxillo from New Mexico, tried to make it clear that he wasn’t really advocating sudden separation, but that the emergence of a sort of Hispanic “Quebec” was likely in the next 50 to 100 years. Of course, a lot of people denounced this, including many Chicanos who felt his motives were actually “Eurocentric”.
Yet this have been seized upon by some right wing groups, who claim that Latin American immigration and multiculturalism are driving a mass “Aztlán” speratist movement, that seeks to drive out whites and return these lands to Mexico, or set up a new “Chicano nation”.
However this is mostly hogwash. Basically a small fringe of Chicano extremists and a small fring of Anglo extremists are essentially jerking each other off with claims and counterclaims of “Aztlán separatism”. I think in 50 years, there will be definitely a political difference in California, Arizona, or Texas (New Mexico is already there), and already there have been cultural changes that do make some people uncomfortable…but if anything it’s Mexico that will be holding out against absorption into North America - and not the other way around.
Also , “Aztlan.net” is very suspicious, as it seems to have more Anti-Jewish rhetoric than anything else. As far as I know its a complete fraud, as not even the most hardcore Chicanistas I know have any such views. I think MEChA is more representative of leftist Chicano activism that makes the case for some sort of political Aztlán, and my personal impression of them is that they are more “Food Court Che” types than a serious threat to anyone.