The Oxford English Dictionary’s official website gives “mestiza” the definition of: a person of mixed origin; originally a man with a Spanish father and an American Indian mother.
The definition that is portrayed by Anzaldua is loosely similar to the one given by the OED, but also, in many respects very different. It differs by, first of all, being more broadened to also encompass American decent as well as Indian and Mexican. And secondly, a feeling of being "lost" in between these different ancestries. Being of mixed ancestries she doesn't have one single land or culture that she can completely identify with or be completely acepted by.
One passage i feel describes this idea of "mestiza" is,
"So, don't give me your tenets and your laws. Don't give me your lukewarm gods. What i want is an accounting with all three cultures-white, Mexican, and Indian. I want the freedom to carve and chisel my own face, to staunch the bleeding with ashes, to fashion my own gods out of my entrails. And if going home is denied me then i will have to stand and claim my space, making a new culture-una cultura mestiza-with my own lumber, my own bricks, and mortar and my own feminist architecture.
I feel that this passage really show her definition of "mestiza," becuase it shows that she has no real belonging to any of the specific cultures and instead of trying to belong to one, would rather be considered her own culture.