The inverted cross originally represented the apostle Peter's humility in his martyrdom. He insisted that he be crucified upside-down, because he felt that he was unworthy to die in the same position as Christ.
Catholic speaker and apologist, Hector Molina explains:
As a result of the manner in which he was crucified, the Church has used the upside down cross (without a corpus, so not a crucifix) to designate Peter, not Christ. The Pope, being the successor of Peter, employs the symbol of the upside down cross as a symbolic reminder of St. Peter's humility and heroic martyrdom. Unlike an upside down crucifix, which seeks to invert and subvert it’s meaning, there is nothing satanic about an upside down cross. - Catholic.com
But today, especially in the rock music culture, it generally represents the opposite: satanism and its mockery of Christ.
Occult symbols are fast replacing Christian symbols in our culture. Check out what these signs and symbols mean from links below: