Final answer:
The movement aimed at securing women's suffrage in the late 19th and early 20th centuries is known as first-wave feminism, focusing primarily on the right to vote and battling against entrenched legal and societal discrimination.
Step-by-step explanation:
The social movement in the late 19th and early 20th centuries that focused on women's suffrage is referred to as first-wave feminism. This movement was characterized by its fight against legally-mandated discrimination against women, including property laws, control over children, and primarily the battle for the right to vote. Women faced considerable opposition, with arguments against their intellectual capacity and societal roles. Notable figures like Queen Victoria were vocal about their disdain for women's rights. However, determined activists like Hubertine Auclert and organizations such as the National Society for Women's Suffrage were pivotal in advancing the feminist cause, with women in Finland and Norway gaining the vote before World War I. Yet, in some places like France and Switzerland, women's suffrage was granted much later, in 1944 and 1971, respectively.