Japanese word for one's aunt or, by extension, any middle-aged woman, and anime fan-speak for the same. Can also have honorifics other than -san, though -san is by far the most common.
The term is also used in Taiwan for middle-aged and older women, though not for relatives. May or may not have anything to do with the Japanese occupation of the island. The rough Korean equivalent would be "ajumma".
When a character in her late 20s or early 30s is called oba-san, she is likely to become flustered or smack the person who referred to her as such, depending on temperament. She may ask to be called by her name instead, or to be called onee-san (meaning older sister, or a woman who is older than oneself but younger than middle age). The male version is oji-san ("uncle"), whilst oyaji is used for significantly older males and is considered somewhat rude (like calling a middle-aged man "gramps") unless it's used to address Yakuza bosses. Occasionally a little kid will call a teenage girl Oba-san, much to the girl's consternation. This scenario is an example of Ma'am Shock; please place examples there.
Not to be confused with "Obaa-san", which can mean "grandmother" or "old woman", though some characters may also have a Ma'am Shock reaction to being called this.