Falshire Field is the location where the last battle between the Falshire Knights, an order of noble knights led by Aelf in defense of the Soulstone, and Florentine's order of rogue templars, took place. We get some impressions of these rampaged grounds during the cutscene , which is triggered upon investigating the Old Knight's Helm in the Mansion's Gallery. The scene shows a fortress of some sort, up on an elevated space off in the distance, while the forefront is filled with several military tents, broken carriages, open fires and arrows, emanating an air of utter defeat and desolation.
The location name is mentioned by Adam during his reflection on Aelf and the Soulstone:
Adam: [Aelf] fell long ago, defending the Soulstone with his Falshire Knights. Fell to Florentine and his demonic hordes at Falshire field.
The prefix fal- could be a reference to the Fall of the Stone, which implies that the naming of the location and the knightly order occured posthumously. The suffix -shire, meaning "care" or "official charge", refers to the British tradition of dividing land into counties, a term which was introduced during the Norman Conquest.
The place is also name-checked to by one of the voices that we hear while travelling through the Tower: