It's an older answer, but u/Iwashmyself had a quite engaging answer on this question in this thread.

The question of why "revenge" is not for me to answer, but I have several past answers on Queen Anne:

What was King James II relationship with his two daughters?

Queen Anne of England was pregnant seventeen times yet had no children reach adolescence. Was this high rate of child mortality standard in all social castes at the time? Or is it more likely due to centuries of inbreeding by the royal families of Europe?

Is the movie ''The Favourite'' Plausible?

A lot of good replies and links to other posts, but I feel like a concise explanation would help you out. A lot of those posts are made with the presumption that you have an understanding of Jacobitism and Queen Anne. I’m a political science student and have general knowledge of political developments at the time

Queen Anne was Queen of Great Britain (which was created as a unification of the kingdoms of Scotland, Ireland and England under her rule) and was the last ruler of the Stuart dynasty. The Stuart Dynasty at the time time was seen as largely pro-Catholic which was contentious in Britain which was majority Protestant at the time, in fact Queen Anne’s father James the II (of England) and VII (of Scotland) was openly Catholic was deposed in favor of Anne’s older sister who was Protestant. Her older sister died without children and the throne passed to Anne.

The Act of Settlement was passed in 1701 under Mary II, Anne’s sister, to resolve the future succession as neither Mary or Anne had children at the time. The act had the effect of excluding Roman Catholics from future succession to the Throne and disinherited all Stuart descendants ( (besides Anne who was seen as acceptable due to her Protestantism) of Charles I (who was seen as a tyrannical king with Catholic sympathies and who started the English Civil War).

After Queen Anne ascended and died, the throne passed to the distantly related George of Hanover who was a German prince and closest Protestant in the line of succession. This was the end of the Stuart Dynasty and the beginning of the House of Hanover (which would rule until Queen Victoria).

The rest of the disinherited Catholic Stuart Dynasty, however, continued and still claimed the throne. Supporters of this dynasty and the movement for them to reclaim the throne were known as “Jacobites”, with Jacubus being a Latin rendering of the name James who was the one who claimed the throne.

Jacobitism was popular in varying degrees amongst lower classes of the British, and nominal supporters would often toast to the Stuart king’s name rather than the legitimate Hanoverian king. This was also true of British who were abroad. A variety of pirates would name their ships in honor of the Stuart monarchs and the Jacobite cause, and some even opened relations with the Jacobite court in exile to give them nominal justification for pirating British Ships (who they saw as being under the control of the illegitimate Hanover monarchs).

Blackbeard’s ship, Queen Anne’s Revenge, can thus be seen as a way to harken back to the last Stuart monarch. Whatever the “revenge” would be is open to interpretation, possibly it refers to the last bit of fury and revenge her dynasty is enacting through Blackbeard’s piracy.

Sources:

https://www.royal.uk/act-settlement-0

https://www.academia.edu/772352/Jacobitism_and_the_Golden_Age_of_Piracy_1715-1725

Edit: accidentally referred to James II as William III

Edit 2: Ireland was kept as a separate kingdom ruled in personal Union until 1801 as someone else corrected me on