A Persona or Demon's type and subtype determine its strengths and weaknesses. As both Types and Subtypes come in pairs, the Persona or Demon will somewhat resist their Type and Subtype (resisting, absorbing, nullifying or repelling it) and be weak to their Type's opposite. For example, the Demon Ganesha is of the Wind Subtype, meaning it resists it somehow (in Ganesha's case, by repelling it) and of the Element Type, meaning it is weak to Force attacks. Also, Types and Subtypes also determine the spells that a Persona can inherit via fusion: Personas of the Element and Force types cannot inherit spells that oppose their Subtype; Personas of the Light Type cannot inherit spells of the Death Subtype and Personas of the Dark Type cannot inherit spells of the Expel Subtype.
The PlayStation release uses English names for the Types and Subtypes, which were left as-is in Revelations: Persona. The PSP port, however, uses Japanese names.
In Persona 2, Personas and Demons have Types but not Subtypes, however unlike the previous game a Persona or Demon's type does not give it inherent resistances or weaknesses, and only seems to restrict which skills a persona can learn from Skill Cards. The number of types is also reduced to just the 4 Element types or "None".
Element and Force, as well as Light and Dark, oppose each other.
Fire and Ice, as well as Wind and Earth, oppose each other.
Electric and Nuclear, as well as Gravity and Blast, oppose each other.