When one word or concept is placed at each corner of a triangle, there is a special property. Each word or concept will affect the other two. In Mahāyāna branch of Buddhism, the three components of enlightenment Insight (見地) Practice (修證) and Vows (行願) can be placed in such a way. In this post, I shall briefly tackle their relationships. My approach is Zen (and Tao), without apology, and certainly is far from definitive.
When we talk about Practice in Zen, we have in mind of Zazen (坐禪), or meditation. Meditation however is a common practice for many schools of religious, spiritual and health related (both physical and psychological) disciplines or practices. The special thing about Zen meditative practice is that a proficient practitioner is supposed to be able to get into a certain meditative mode or state while walking, living, sitting and sleeping (行住坐卧).
Koans are special tools related to Zen Insight. They are like case studies. And the Insights are imbued or embedded inside the stories. These stories are oftentimes examples of successful and unsuccessful insights, both are important (for example in the famous story of "Monk slaughters a cat" [NANQUAN KILLS A CAT (南泉斬貓)] one monk got the Insight while the other monks could not). Understanding the koans presupposes the students to have understood relevant theories of the relevant Sutra. Koans are like case studies in business schools. It is easy for students to mistakenly think that they are enlightened/having got the Insight after "understanding" the logic behind the story. The gist of the matter is that the "story" facing each individual will be his personal story of tomorrow. Understanding helps but the test is always our "personal koans" of tomorrow. To take the business school analogy further, having high GPA does not guarantee a student being able to make good business decisions in future. It is always the next decision to judge whether a manager is a good manager.
Now we can answer the question of "How is Practice relevant to Insight?" The simplest way to explain is that with good meditative practice one can be in a better position to be able to do the right thing when one faces one's "personal koan" tomorrow. And likewise, without Insight, a student's Practice will have no influence to what define an enlightened person.
Then "How is Vow relevant to Practice?" The simplest way to put is that Vow is a means to direct one's meditative practice into a deeper zone (as a comparison, free divers have to be trained under different guiding principles to go into deep meditative zone, Without a guiding principle, be it Buddhist Vow or free dive hurdles, going into deep meditation is unnecessary). For common folks (like most of us) who do not intent to make Bohsavista Vow, a simple vow to be more compassionate towards people around us can give us good training direction (and motivation) to our meditative practice.
Further analysis is possible but will probably bring my readers into a purely intellectual journey outside the realm of Zen which will defeat the whole purpose of writing this post.
(edited on 26 Jan 2016)