I’ve come across this description of Sharia in the comments of one Internet user about a month ago. I like it, because it is concise but comprehensive.
Sharia is a set of laws that are based on both scripture and tradition. It is basically codifying how being an Islamic society should look in law and conduct. There are some aspects of Sharia that are based on the same principles espoused by conservatives in many other religions and other parts that are totally disgusting to anyone who cares about freedom, particularly for women. The main differences between western law and sharia is the outrageously cruel punishments, the overreliance on eye witness testimony rather than contracts or physical evidence, the second class status of women, and forced participation in religious practices.
Conservative Christians share many of the same ideas but I have never heard a Christian advocate that lack of compliance with Christianity be punished with anything other than eternal hellfire. Sharia calls for death, flogging, stoning or imprisonment for thought crimes and whatever is deemed to be immoral.
In order to support Sharia, you must be completely opposed to civil rights. In fairness, only a few countries practice it in full and some Muslim countries do not adopt the most severe parts, only apply it to Muslims, or only use it for dispute resolution in civil cases. Either way, Sharia is totally disgusting for any person who cares about liberty and it is the best argument for church state separation ever made.
Any Muslim who supports it is despicable, any person who lives under it is terribly unfortunate, and any woman who supports it is absolutely insane.