꺾다 is bending or snapping something at an angle: 발을 좀 이렇게 꺾어주면 훨씬 낫다고 "it feels much better if you bend your foot like this," or curling the tongue back in the throat to pronounce a consonant. It extends to putting a sudden turn into a melody — the ornament in Korean folk singing is 꺾다 ('아라리가 났네~에↗에↘에~' 이렇게 꺾는거 있잖아요), and 이렇게 꺾는 게 중요한데 is someone teaching it. It also covers twisting something out of shape, as when [문제를 짓궂게 꺾은 제작진] bend a quiz question. Most lines pair it with 이렇게 because the speaker is demonstrating.