This names the quality of having a clear aim, and of moving toward it. A person with purposefulness knows what they want and does not drift. You can also talk about the purposefulness of a plan, a walk, a look, or a whole life: it all points somewhere. The word is a little careful — teachers, bosses, and writers like it — but it is not legal English. In everyday talk people more often say someone is purposeful, or that they have a purpose. This -ness form shows up when you want to name the quality itself, not the person. Though actually, it does not always mean 'strict' or 'cold'. A kind teacher can work with great purposefulness; the word is about direction, not about being hard.