It is the female equivalent of "sir". Children usually call their teacher "ma'am"; employees often call their boss "ma'am". HOWEVER, be careful. In very generalized, stereotyped terms: Boys are usually very proud the first time they are called "sir". It means they have earned your respect. Young women are often shocked the first time they are called "ma'am". It means that they are no longer young and beautiful, and people are now thinking of them as a mother or as a professional instead of as a potential marriage partner. Of course, in the right context a girl might be happy if you call her ma'am, and in the wrong context a boy might not be happy if you call him "sir", but in general "ma'am" is a more dangerous word than "sir". Use it with caution. Lastly, the word is very common as a respectful address for all middle-aged and older women in the American South and Midwest, but it is much less common in the Northeast and on the West Coast. There, only use "sir" and "maám" if you are talking to your professor or your boss.

I think we use "Madame" for that purpose (e.g., "Madame President," or "Madame Chairwoman") "Madam" is used as the female equivalent of "Sir" in certain contexts. They both sound the same.

@su.ki. In America we also use 'madam' but only for government officials who are women, as far as I know

The answer Chris has given is true for North America. Bodyguard is a British series, however, and the usages are different here. In the UK, 'ma'am' is NOT the everyday feminine equivalent of 'sir'. [The equivalent of the American usage of 'ma'am' is actually 'madam' - a term of address used in BrE alongside 'sir' in everyday contexts in service industries. For example, a flight attendant or hotel receptionist would address adult female guests as 'madam' - never 'ma'am'] 'Ma'am' is rarely used in 'civilian' contexts in Britain. It is mainly used in military and police contexts to address a higher ranking female officer. This is why people in Bodyguard use 'ma'am' when speaking to to high-ranking women in the police and secret services, and why David Budd (in his official role as protection officer) uses 'Ma'am' to speak to his female bosses in the police and government, including the Home Secretary. Members of the royal family (including the Queen) are also addressed as Ma'am.