Why would the corner of some foreign field become England if Brooke should die?

Brooke's poem is an expression of his belief that during World War I (and also, implicitly, in earlier wars) the English soldier was fighting more for an ideal than simply out of obedience for the demands of his country.
For centuries, England has seen itself as a country in which freedom and individualism have flourished. The US, and all the English-speaking peoples throughout the world, have inherited the same mindset and the same conviction. In anticipating his death on a foreign field, the speaker is stating that since he will have died in order to perpetuate these English ideals, a part of England will have been figuratively planted in the soil. The "dreams, happy as her day," and the "gentleness" are the essence of England.
After the unprecedented carnage of the Great War, Brooke's verse, which seemed to idealize warfare, was often seen as unthinkingly representative of foolish slogans like "my country, right or wrong." Britain, Europe, and the world overall were so shocked by the scale of death that pacifism became for many an absolute ideal, cancelling in their minds the fact that in many cases war is unfortunately necessary. Though in retrospect "The Soldier" does sound naive and sentimental, it encapsulates the central thinking that has motivated not just British men in combat, but all soldiers throughout history.