The same as in civvie life.  It's a completely subjective term meaning anything that will complicate matters unnecessarily and negatively.

When people say this, what they mean is that they want a simple, pleasant, cut-and-dried transaction without any extra emotional baggage.  However, "drama" for one person could be routine for another, depending on tolerance levels.

When you've seen it used here, was it used by providers or clients, or both?

It's a bit hard to explain but I'll try:

It's seems that from time to time there is a, misunderstanding, to be euphemistic, between people in the hobby.

It could be between two providers, a provider and a hobbyist, and sometimes even between two hobbyist (we're only flesh and blood.)

The reasons for the drama vary considerably.  It's usually of the "Someone told me that somebody said this or that about me or my friend and.....they can go fuck themselves."

The good thing is that after a few days the whole thing blows over and we can all get back to the business at hand.

If you are ever in a situation where someone is venting to you about their latest drama, the best thing to do is just nod intently and keep your mouth shut.

As the great emancipator said in his farewell speech just before leaving for Washington on the eve of his election:  "This too, shall pass."