"Drama" can mean a situation where there is a lot of negative emotions being experienced by the people involved. People say "I try to stay away from drama" when they mean that they like to avoic situations like that. :]

it could mean the attitude or emotions portrayed by the person regarding a situation.

If you wanted to carry out something quietly without a lot of fanfare, you might also tell someone "Let's get this done with as little drama as possible...".

One meaning is the one of "dramaqueen" it's someone who displays alot of emotions often regarded to be more than the situation motivates.