When we're dealing with words, the right way to start is to first look at the reality they're supposedly referring to ... rather than arguing about the 'correct definition'.
In the US, but not only the US, we've had the growth, over the last couple of decades, of a certain attitude towards society. This attitude has something in common with the view of the traditional Left, but is really something new. It's a bit hard to define, so I'll fall back on what a Supreme Court justice once said about 'pornography': hard to define but you know it when you see it.
So let's look at an example: traditionally, both Left and Right recognized that humankind is divided into many different societies, AND, that some of them, judged by things we all consider good, such as the extension of the human life span, are in advance of others. Some societies are 'advanced' and some are 'backward'.
Read the
Communist Manifesto, published in 1848, and you'll see Marx and Engels praising capitalism for dragging the 'barbarian' and 'semi-barbarian' nations into modernity. Those are their exact words (in English translation). [Of course, the idea that economic/technical/scientific progress simply causes social progress is wrong. They are loosely coupled, but no more than that.]
Now, suppose I was a college professor in the US, teaching about 'imperialism'. And suppose I agreed with Marx and Engels, and said that not everything the imperialists did in the backward countries was bad, and that their getting their independence from the colonialists was not all good.
For instance, I might refer to the fact that when the British colonialists ruled Jamaica, it had one of the lowest murder rates in the world (3.9 per 100 000). They left, and now it has one of the highest (62 per 100 000 in 2009). [
Jamaica - Wikipedia]
Now, if I had said that, say, 25 years ago, I could have expected someone to attempt a refutation. Perhaps something similar happened when the Americans became independent. Perhaps it's due to some economic reason -- maybe Jamaica enjoyed some special status under the British empire which it lost when it left, causing economic disruption, etc. It would be an argument. You would be able to decide which side, if either, was correct.
But now ... 'woke' mobs would demand that I be fired. (If I wanted to be smarter, I would refer to Jamaica's backward attitude to homosexuality -- male homosexuality is punishable by imprisonment, and there are mob attacks against gays. But even then, I suspect, the 'woke' mob would want my head.)
So that's 'woke': the attempt to suppress views that they don't like, including by violence. The 'anti-racism' stuff is superficial -- those attitudes are shared by all civilized people.
This won't get better. And it's why conservatives/patriots had better wake up, and start preparing for what's coming. Societies whose intelligentsia despise them, and who are in the grip of what is, in effect, fascist attitudes to speech and thought they don't like, are not going to last.