The term "demigod" does not refer to a singular race. Rather, "demigod" is a term used to refer to a group of individuals (generally from Magical races) who are worshiped as lesser deities.
Note: Sometimes, however, the term "demigod" is used to refer to a half-breed of a Magical creature with a Non-Magical creature. This is a misnomer; these half-breeds, while incredibly powerful by Non-Magical standards, have strength more akin to a Monster than a Magical creature.
Demigods are generally individuals of note, with histories and mythologies all their own.
Since Demigods are varied individuals,they all have their own abilities. However, generally speaking an individual doesn't become deemed a demigod without some impressive magical ability, meaning these individuals are often some of the oldest and most powerful Magical creatures in existence.
Because demigod is more a title bestowed by others, all demigods have one other trait in common: they interact (or have in the past) with other races, generally of the Living Realm.
Demigods are, generally, not prescribed a domain. Often, however, they will be well known for a skill or origin story.
Every culture has it's own takes on the mythology of the commonly known demigods, as well as their own list of lesser demigods.
Note: It is rumored that Queen Ratha of Kelir is a Demigod; half Elven, half Celestial. She denies this.