How was the suffragette movement of Britain part of the spread of democracy in the 20th century?

You'll have to clarify where you mean by "spread of democracy." America? Russia? China? But sufragettes often made appeals to universal rights of man, especially the right to vote, that is at the center of democracy now. Sufragettes in Britain occupied a privileged position, too; they were part of one of the great imperialist powers so, despite the fact that they were marginal, their influence reached the rest of the world because of the fact that they lived in a superpower upon which the sun never set.