Someone’s demeanor is his or her outward behavior, or the way he or she appears to others. It is spelled demeanour outside the United States. The spelling change extends to misdemeanor and misdemeanour.
Side note: The United States borrowed the word misdemeanor from the United Kingdom. Misdemeanor adds the prefix mis- which denotes that the subsequent action has been done wrongly or badly (e.g., misheard, misread, misunderstood). In the United Kingdom demeanour was also a verb, so a misdemeanour was a wrong behavior towards others.
Other English-speaking countries have changed the legal term of misdemeanour to other classifications, but the term is still used when describing a crime, especially ones committed in the United States.
Examples
A co-worker at UVa said Matthew’s demeanor changed the week after Graham disappeared. Typically jovial, she said, Matthew became reserved, and began taking his lunch break alone. [The Roanoke Times]
An 0-3 start that includes one of the most humiliating losses in franchise history is enough to alter the demeanor of even the most stoic of coaches, but Smith’s players say he has yet to lose his cool. [Tampa Tribune]
His Holiness said he has heard from a former Indian minister who met Xi Jinping in Brazil that he is not like previous leaders; he has a more humane demeanour. [Tibet Post]
They played like they knew there was another game after this one. And that preparation and demeanour will be important this week. [Daily Telegraph]
Brown pleaded guilty to misdemeanour assault and was sentenced to time served. [Hamilton Spectator]