They're referring to the overthrow of the elected government in 2014. That government was relatively friendly towards Russia. The US was involved[0] in the revolution/coup (whatever you want to call it, though a lot of people in eastern Ukraine considered it a "coup"), and the Russian government saw it as an attempt to bring Ukraine into the orbit of the United States.
Whatever you think of Yanukovych and the people who followed him, the US getting so heavily involved in a country right on Russia's doorstep was a very risky move. There have been warnings from several prominent American foreign policy analysts about how this sort of action would prompt an extreme reaction from Russia. George Kennan, the father of the US' Cold War containment strategy, was extremely prescient, all the way back in 1998:
> "Of course there is going to be a bad reaction from Russia, and then [the NATO expanders] will say that we always told you that is how the Russians are - but this is just wrong. [...] This has been my life, and it pains me to see it so screwed up in the end."[1]
If both Russia and the US continue to push maximalist positions, this conflict will just escalate and escalate, and nobody can say where it will end.
0. Recorded call from 2014 between high-level US State Department officials, in which they work out who should go in what position in the Ukrainian government: https://youtu.be/JoW75J5bnnE
1. George Kennan discussing NATO expansion in 1998: http://www.nytimes.com/1998/05/02/opinion/foreign-affairs-no...