The expression “elephant in the room”, sometimes also “elephant in the living room”, means “a big issue everyone is aware of, but which is being ignored, because everybody finds discussion about it uncomfortable”. The rationale behind the idiom is that an elephant in a (living) room would be impossible to overlook, but people in the room can nevertheless choose to behave as if the elephant was non-existent. For example:
Increasing poverty in the world is the western politicians’ elephant in the room.
The fact that his 35-year-old brother was still living with his parents was a big elephant in the room at every family gathering.
By the way, if you haven’t read my guide on how to avoid the most common mistakes in English, make sure to check it out; it deals with similar topics.