During the 1960s, there was a huge stirring among various social groups to rise up and fight for their rights against an American government and society that didn't acknowledge or prioritize them. We all know about the Black Power movement, but not nearly as many of us know about the Chicano Movement that started around the same time.
Mexican-Americans were a completely disregarded group in American society, and were called Chicano as a racial slur. But much like the Queer community has done with the word queer (and many others), the group reclaimed the word for their own use. This patch, and others like it, showed your support in the fight for human rights and dissolution of discriminatory systems affecting Mexican-Americans. Although you can get these kinds of patches for under $10 because a ton of them were made, they represent a highly important piece of history.