Woke is meant another way for describing someone who is enlightened and has a greater understanding of social injustices. However, in the context of Twitter, "Woke Twitter" are those who will chastise, reprimand and criticise those who often make sexist, racial, homophobic and classist remarks.
Woke twitter is very complex to explain, it is better to experience it for yourself. Be careful not to cross them, however, because they are ready to school and put those in their place who they think have overstepped.
It's not easy being woke though...
Others feel that the instigators of woke Twitter have a superiority complex only interested in forcing their opinions others.
Sometimes woke twitter even gets too woke: