Holiness has never been adequately defined. Some define it as separation, as in a separation from the profane. Some define it as dedication or consecration to use in God's service. These definitions do not even come close to describing the impressions that surround us when we perceive the Holy. The best definition I have yet heard is that holiness means being indwelt by the glory and presence of God. This, at least, captures some part of the profound beauty, awe, and wonder that we typically sense in the presence of the Holy.
There is no doubt some reason for those who see holiness as a separation from the profane. The ancient call was to "Come out from among them and be separate." Many Christians will think of the ancient Jewish Temple and tabernacle with their careful regulations for purity and separation. Still, here again in the Temple and the tabernacle we definitely see places that are indwelt by the glory and presence of God. They were special places to come, places where even the omnipresent God was specially and particularly present for his people -- or perhaps just particularly evident and accessible, places where God had chosen to reveal himself, chosen to meet with his people.
In Jesus, we see the presence of God on earth in a way that we have never seen before. The very idea that here in a man we have Emmanuel, God With Us, threatens and challenges the idea of a separation between sacred and profane. While the the previous separation of sacred and profane protected the sacred by giving it its own dedicated and inviolable space, it also in some measure protected the profane by confining the Holy. Here in Jesus of Nazareth we see holiness moving to challenge the profane on its own ground. As the ancient Temple was destroyed and there was apparently no more safe place for holiness, God had left the Temple and had made his people into the living stones of the new temple. Now there was no more safe place for the profane.
In Jesus, we see God's movement clearly: he sought out people that were by no means holy, and these he called to a new life. The low, the profane, the outcast, the vile and despicable of society -- these were the ones he sought out. Holiness did not depend on the beauty of the raw materials but on the power of the love of God. Out of people who were nothing, he created us and called us to be holy. And for these redeemed, the call was not "Come out and be separate," but instead "Go into all the world."