The phrase you mention in your question comes from one of the most well known and recognized passages in Walden, by Henry David Thoreau. He explains:
I went to the woods because I wished to live deliberately, to front only the essential facts of life, and see if I could not learn what it had to teach, and not, when I came to die, discover that I had not lived.... I wanted to live deep and suck out all the marrow of life, ...to drive life into a corner, and reduce it to its lowest terms....
Of course Thoreau went to the woods to live a life of relative solitude so he could decide what was important in life and what was not, what the "essential facts of life" were and get rid of the rest.
Thoreau articulates this same theme throughout his entire journal/book, and here is another famous clarification of his philosophy:
Our life is frittered away by detail. Simplify, simplify, simplify! I say, let your affairs be as two or three, and not a hundred or a thousand; instead of a million count half a dozen, and keep your accounts on your thumb-nail.
The repetition of that key word, "simplify, simplify, simplify," expresses Thoreau's beliefs perfectly. In Walden he was proud to keep records of how little money he spent to live, of the things he observed when he had the time to watch, and of his recycling of previously used materials. Life should not be spent accumulating things or going too quickly to appreciate what we have, says Thoreau.
The quote you mention suggests life and all the "stuff" of life should be pushed into a corner until only the essential things are left.