"Woke" is the past tense of 'wake', and used in the sense that some people have 'awoken' or become aware of historical facts and history which others, usually holding rigid and conservative views, would prefer to be kept quiet.

Thus for example, the National Trust is now revealing how the original owners made the money which allowed them to build the grand houses the NT now curate. The fact that this money may have come from slavery in the former UK colonies is something those who hold anti-woke opinions would prefer be left unsaid.

Similarly petitions to the British Museum to return certain items in its collection to the original country is considered 'woke' by some.