In this use, singleness is great determination when you are working toward one thing: a mind that does not split. You will almost always meet it in the set phrase singleness of purpose, and sometimes singleness of mind. On its own, without of purpose, English speakers much more often use singleness to mean “not being married,” so this “determination” sense really lives inside that one phrase. It sounds formal and a little old-fashioned; many people would now say focus or determination instead. Though actually, it still turns up in speeches and serious writing, because it has a high, earnest tone.

目標專一、一心一意（幾乎只出現在 singleness of purpose；單用 singleness 在英語裡多半是「單身」）