The concept of La Chingada is difficult to explain. Its origin is the verb chingar which is used in Mexico in the sense of violation, sexual penetration, and domination of the female on the part of the male.

If you know Spanish, you may want to link to this website which provides a good glossary of the different manifestations of the word, including various uses of the verb, and the nouns and adjectives that derive from it.

http://www.baja.com/chingada.htm