Egyptian law allows for any random citizen to make such a complaint against whoever they choose. This is how pop singer Shyma ended up being jailed for a year for "suggestively eating a banana" in a music video. Another singer was arrested for a pretty tame video whose title rhymes with an insult.
While the average Egyptian isn't losing any sleep over these things, some concerned citizens have made a career out of tattling on celebrities. In Youssef's case, it was two lawyers named Samir Sabry and Amr Abdel Salam, who gained notoriety for suing belly dancers and "potty-mouthed" puppeteers and publicly attacking foreign visitors for "insulting Egypt." Said foreigners were also women, in case you were starting to sense a pattern here.
The charges against Youssef were dropped after she apologized for her fashion crime. Matters were presumably helped when word got out to the international press and the lawyers behind it all became global laughingstocks. That's not to say you should go and seek your fortune by performing on the streets of Cairo with belly-dancing sex puppets any time soon.