Shariah law is Islamic law. I’ll try to explain in a sec, but first I must put in a word here. There is no way that any serious Muslims want Shariah law implemented in the United States. This must be some sort of fringe Wahhabi (extremist) group. Shariah law can only be implemented in a place where the majority of people are Muslim. Otherwise, it’s pointless.
In Islam, there are two types of religious law - Shariah and Fiqh. Fiqh is personal law. Fiqh describes how to pray, fast, what is a sin and what isn’t, etc.
Shariah is the public law. Shariah allows a government that follows Shariah law to determine public laws, issue punishment, etc. For example, murder can be punished one of three ways. The murderer can be killed or the family of the man murdered can demand diyyah (blood money) to compensate for the loss. If diyyah is payed, the murder faces no more punishment (mind you, the victim gets to decide the amount of diyyah - so don’t think of it as the easy way out). The final way is for the victim to forgive the offender. This actually goes for many victim related crimes. Assault, rape, murder, accidental injury, etc. There is a punishment (death, flogging, etc), or the victim can demand diyyah, or the victim can outright forgive the offender. That’s the basic idea behind Shariah. It goes into a lot more detail, but that’s the basics.
One common misconception about Shariah is that Christians and Jews are persecuted under it. This is false. Under Shariah (true Shariah - not what Saudi Arabia has to say about it), Christians and Jews are protected minorities. They have the right to celebrate their holy days, construct and worship in their churches or synagogues, etc.
But again, any serious Muslim would not desire Shariah to be used in the United States. That’s really silly. This group is a Wahhabi fringe group, most likely. ** Pay them no attention. **They thrive on attention and controversy. If you don’t give it to them, they will eventually stop saying and doing things (9/11 anyone?) for the shock and awe value.