Literally meas "Mother Fucker". Typically expressed in a moment of dispair, impatience, disbelieve, etc. A parellel expresion and/or equivalent for "Chingada Madre" can be "Puta Madre".
1. Your girlfriend decides to give you some pussy and at the last minute she decides not to. With your eyes of disbelieve you stare at her and say "Chingada Madre".
2. You walk in a bus, look for change to pay the fare and find out you are short on change. Then you say "Chingada Madre". Be aware that most likely the bus driver will stare back at you in disbelieve and will also say "Chingada Madre".