The RO portion will only remove a portion of all contaminents in a given water supply..this is accomplished through water being forced through a thin membrane filter...
The DI either stand alone, or portion removes all negative and possitive ions from the water. This is done through absorbtion...their are primarily 2 (that I know of for standard home use) types of resins...anion and cation...one does the positive ions and the other negative.
The DI works pretty similar to a water softner for a home, instead of charged rods...it uses the resins.