What was the significance of the speech "Freedom or Death" by Emmeline Pankhurst?
In your question you are referring to this British suffragette's most famous speeches. Considering she is a British suffragette, you can be sure that her goal was to allow women the vote in Britain. It wasn't that long ago that Time Magazine named Pankhurst as one of the most influential women of the 20th century saying the following:
[Emmeline Pankhurst] shaped an idea of women for our time; she shook society into a new pattern from which there could be no going back.
I am going to attest that Emmeline Pankhurst was vastly influenced by her activist parents (both active in the political scene in England). In her elder years, she became a notorious traveling speaker (after having sold her home). In fact, it was on one of these traveling tours that she gave "Freedom or Death" (a semi-allusion to Henry's "Give me liberty, or give me death" speech).
Interestingly enough, the speech "Freedom or Death" was given in the state of Connecticut in the United States. This fact alone shows that Emmeline Pankhurst was influential in more than her own country and has also affected women's suffrage in the United States.
This speech, given in Hartford, Connecticut in 1913, was significant as a strong statement of the position that women's suffrage advocates were putting forth. In a sense, it is like Martin Luther King, Jr.'s "I Have a Dream" speech, though it is much less well-known. In both cases, the speeches encapsulated the thinking of a major social movement.
In this speech, Pankhurst lays out her motivations for pushing for suffrage in her particular way. She justifies the tactics that she and the other suffragettes have been using in England. She declares their determination to fight to the death (she meant this literally because one of the tactics used by suffragettes in England was going on hunger strikes when in prison) in order to try to gain the right to vote.
The speech, then, is significant as a statement of goals and a vindication of the means being used to achieve those goals.