Probable cause means that a police officer must have a reasonable belief that a crime has been, is being, or will be committed before they can make an arrest or search someone's home or car.
When a police officer sees something that looks like it could be a crime (like someone running away with someone else's purse), they can search that person or their car to see if they have stolen something. They can also arrest that person, because the officer thinks that it is likely that the person committed a crime. This is called probable cause.