To be a new creation means that you are a new being. As a new being, you are totally free from the past and everything to do with the past. The Twentieth Century Translation of 2 Corinthians 5:17 says, "If anyone is in union with Christ, He is a new being!...

The Living Bible says, "When someone becomes a Christian he becomes a brand new person inside. He is not the same anymore. A new life has begun!...

Phillips translation says, "...He becomes a new person altogether - the past is finished and gone, everything has become fresh and new."

The new "being" is your inner man. Your Spirit is the real you, your true self. When you were born again, this real you or your true self, your spirit (the new self), became a new creation. At that time you received eternal life. This eternal life is the nature of God (2 Peter 1:4).

The great thing about understanding that you are a new creation is that the person you used to be is gone. Laubach says, "The man he was has passed away, and, behold, a new man has been created." 

The "old things" means the old being, the old nature, the old man, or anything pertaining to the sin loving nature. Once you are a new creation, you don't even have to deal with the "old man", because he is dead and gone! The old man was the old self you used to be before you became a new creature. Once that revelation becomes a reality in your life, nothing can hold you back!