1) Making a situation more awkward by mocking how awkward it is. The situation need not be awkward in the first place.
Apparently coined by Washington Post columnist Monica Hesse.
2) Mocking someone in an awkward — and thereby probably unsuccessful — manner.
Apparently coined by then-Columbia Journalism Review assistant editor Megan Garber.
Someone asked to define the word "awkward" will often resort to describing the task as "awkward," which is just mockward. When someone does the same with "mockward," it's meta-mockward.