She is mean = "mean" is the adjective and in this sentence it is describing someone's personality. "I don't like Mrs. Jones because she is mean." She is being mean= this is describing behavior that is occurring right now. Her behavior or the way she is acting at the moment is mean. "Mom, Billy is being mean to me."

" She is mean " and " She is being mean " are pretty much the same in definition but the first one is referring to someone's permanent adjective .the second one is referring to what did someone's adjective look like just a while ago or now .