An acronym for "Subject Matter Expert". Generally a person designated as the expert in a particular technology, process, or subject area within a company or organization. Often the title is an oxymoron and is given through a bureaucratic process where the person designated as the so called "expert" knows less about the subject than others yet insists on inserting themselves into the decision making process despite their inferior knowledge. They derive their power via their title rather than any actual factual information they may know.
The IT department can't install Chrome because the Browser SME declared that no more than 2 browsers will be supported and he choose IE and Firefox. He didn't provide any factual basis for his decision when it was announced but he did note that he was the browser SME and thus everyone had to abide by his decision.