I thought this was a very interesting question to ask, because in my personal opinion it depends on the writer. Poems come from ideas, thoughts, dreams, and visions. Poems come from an imaginative mind, with the skills that take those thoughts and dreams, and place them into words down on paper to create what we call a poem.
You use every force of you mind to create a poem, as one guy said in the video, writing poems takes patients, it not only uses your conscious mind but also your unconscious mind. And sometimes when you're trying to understand your unconscious mind and make since of it, it takes time. Another quote that stood out to me in the video was that even though the rational mind is at work, its not running everything. Your ideas and thoughts are a huge impact to your poem, although your mind might be thinking it through rationally, its not doing all the work, your visions are helping it along to create something that makes an awesome poem flow.
My favorite part about the video was the poem that Alice Walker wrote/read. "How poems are made" She begins by saying she understands how poems are made, there is a place where fear, choices, and loss must go. She called it the leftover love. I loved that line, it was very powerful to me and it struck my interest immediately. Poems are about those things that mean something to you, a poem comes from someones mind, and heart. A good poem in my opinion has feeling, has meaning, and has emotions. She goes on. Then she gradually comprehends how poems are made, there the tears that seasons the smile. Another one of my favorite lines, it just captivates me every time i read it because i feel it. It makes since to me that way.
Poems come from within, through reason, thought and imagination, and leftover love.