The term is best known in Northern Ireland. Cardinal Cahal Daly famously called it "the commonest form of moral evasion in Ireland today", though the invention of the term is often attributed alternatively to Daly and to John Hume. (I don't know which is correct).
The best description I have found of what 'whataboutery' is and why it matters comes from Mick Fealty of the excellent Slugger O'Toole website, back in 2005, which is well worth reading in full. He writes of 'whataboutery' that
Evasion may not be the intention but it is the obvious effect. It occurs when individuals are confronted with a difficult or uncomfortable question. The respondent retrenches his/her position and rejigs the question, being careful to pick open a sore point on the part of questioner's 'tribe'. He/she then fires the original query back at the inquirer.
Historical subjects can be the worst. Rational perspective disappears and opponents are forced to assume moral responsibility for their community's past sins. The substance of the issue is foregone for an emotional power play that comprises the solipsistic concerns of the participants, with little regard for fact or quality of argument.
I also hope John Hume's frequent use of the term helps to get across the point, which may be misunderstood, that criticising 'whataboutery' does not mean sitting on the fence and taking some median point on every disputed question. Hume was a moderate nationalist leader, whose ultimate goal was a united Ireland. But he was politician - in the very best sense of the word - committed to dialogue, politics, the building of mutual empathy and a political resolution of the conflict between communities.