One of the interesting aspects of the new usage of the word drama is that it is close to becoming an autoantonym, a word that is used in two opposite senses.

According to Webster 1913, drama describes something that is:

a series of grave or humorous actions of more than ordinary interest, tending toward some striking result
If you look at the modern usage of "drama" amongst young people, it usually means something that is not grave, is not of any particular interest, and has no actual result. It means something petty, predictable and pointless. Of course, it could be argued that "drama" is not an autoantonym, but rather just a term used with irony, since it is often used to refer to someone being overdramatic or melodramatic. Over the several years that the term has been popular, it has seemed to evolve from being a pointed commentary to just being the standard term used for any type of interpersonal conflict. It seems that it is used with no specific reference to the fact that it is ironic. So, if this piece of slang sticks around, the word may be used in coming decades to refer to both the grand and the petty, with people forgetting the original connection between the two.