The verb you use when somebody does the increasing, as against 늘다 and 늘어나다, where a thing grows by itself. Mostly it is physical stretching, and these lines are full of exercise instruction: 보통 무릎을 접어서 발목을 뒤로 잡고 이렇게 늘리세요, 들이마시는 숨에 척추 길게 늘렸다가. It also stretches a sound out — 소리를 이렇게 길게 늘리는 거 — and raises a number: 그리고 내년에는 significantly하게 늘리겠다.