The term “wholly other” is used in Christian theology to describe the difference between God and everything else.  God, the Christian God, is completely different than all other things that exist.  God can be described by essential properties such as holiness, immutability, etc.  But we have to ask how we, as finite creatures, can relate to the infinite God.  It is difficult when he is “wholly other” than we are.  It means that we must relate to him by his self-revelation in the person of Christ Jesus, and through the Bible.