Purity of heart is to will one thing, as Kierkegaard once said. We want to be men whose hearts have become pure, who have discovered a single purpose in life. Because of this many things we could possess simply lose their attraction, for an uncluttered life is what we want.
There are many things we need in order to function in the modern world, and we use some of them in order to be more effective in serving God. At the same time we do not want to be attached to any of them and regularly review our life to make sure we rid it of unnecessary clutter.
This ideal also impacts how our houses are set up, how we use our money, and how we spend our time. So while we are not poor, we seek to be unencumbered and to travel light.