Looking at holiness from the perspective that Hamilton gives, "The distinctions between holy and common and clean and unclean." (Hamilton p. 259), we can conclude that holiness means set apart, different, or distinct.
In relaying this to a new convert, the simplest way would be to explain that God is separate from anything that we have corrupted. As the Egyptians learned, there is none like Him (Exodus 8:10)
Because He is separate from the would and nature that has been corrupted by sin, He is completely pure from any of this corruption.
As His people we are called to be like Him in that way. And we can only do this through the work of Christ, who while retaining His purity made a way that we could be covered with His purity (righteousness). He is also daily conforming us to His image through His word.
This is the basis and the motive to our being holy as He is holy.