When you use the word drama to describe your day-to-day life, you're probably not referring to dialogue and actors on a stage. More than likely, you're talking about some crazy stuff going down. Though drama has taken on a new meaning these days, it has a very specific definition in literature.
In literature, drama refers to a literary work written for performance by an actor or actors. Drama typically consists of dialogue broken up into acts and scenes. There are lots of dramatic subgenres, such as comedy, tragedy, and tragicomedy. A closet drama is drama that's not meant to be performed—only read. We also sometimes also use the word drama to refer to serious, rather than comic, work.
Drama got started way back in the classical period and has flourished in various historical periods, including the Renaissance, the 18th century and Enlightenment, and the modern theater of the 20th century.
What's the difference between drama and theater? Drama refers to the play's text itself while theater emphasizes the performance of the script. That is, theater is all about the stage, whereas drama typically refers to stuff on the page.