Demigods, or Half-Bloods, are superhuman mortals, born of the gods and a mortal, and therefore are half-human, half-god. All demigods wield Demigod Power, connected to the domain of their divine parent and these abilities grow stronger with age. In general they willingly assist their god parent and/or the gods themselves, using their legendary skills and powers. Many have become great heroes, kings, lords, dictators, etc.
While most demigods are created much like regular humans, children of Athena are born from their mother's thoughts merging with their father's. The other gods are likely able to do similar things, however no known examples of similar births are known.
They are escorted to Camp Half-Blood by satyrs (usually) where they are placed into one of the cabins, each honoring a different Olympian.
Most demigods wait forever to be claimingclaimed. Children of Athena are claimed at birth, while others have to demonstrate some form of their parents' trait to be noticed, either through cunning, powers, skills like archery, or even beauty. Otherwise, they are placed in Hermes' cabin, and since he is patron to travelers, anyone is welcomed there, including children of minor gods who aren't important enough to have a cabin. After the Second Olympian War, Percy Jackson had made all of the gods recognize all of their children at the age of thirteen, and that each god and goddess (including the minor gods and goddesses) would get a cabin at Camp Half-Blood and a throne on Olympus.
Demigods are completely indistinguishable from humans. Because gods don't have DNA, they don't have any inhuman traits. They do not have a divine form, however they do inherit some traits from their god parent's divine form. For example, Percy inherited Poseidon's black hair and sea-green eyes and brooding look.
The ichor in a demigod's bloodstream gives them a distinct scent that all monsters can smell and inexplicably attracts them. There are ways to hide or mask the scent, but if a demigod realizes what he/she truly is, their scent will reach its peak. The scent of children of the Big Three is much more potent than that of lesser demigods. Demigods' personalities tend to vary based on their divine parenthood; for example Pesra is reckless and rebellious resembling Poseidon and the untamable seas. Most demigods also have ADHD and/or dyslexia (though it varies from demigod to demigod). Demigods are relatively stronger, more agile, and more durable than regular mortals, and have more resistance to diseases.
Roman Demigods, such as Jason Grace, are an unique subset of demigods who train at Roman Camp Half-BloodCamp Jupiter, which is located near San Francisco. They are born when a god conceives a child with a mortal while in their Roman aspect/form. They naturally speak and read Latin, as opposed to Ancient Greek to Greek demigods, and are trained in the style of the Roman legions instead of Greek warfare.
Roman demigods start their lives at the Wolf House. It is here that Lupa decides if the child is strong or not. She will spend time training the demigod skills they will need to survive. If Lupa believes you are strong enough, she will tell you to follow your instincts to find your way to Camp Jupiter, home of the Roman Legion. However, if Lupa doesn't believe you are strong enough or you show fear, it is said you will be eaten. If you manage to make it to Camp Jupiter, a praetor will decide if you can join the Legion before sending you to have your augury read. If it is favorable, then you can officially join the Legion. Like the Greek demigods, they are unaware of the existence of their counterparts
This is due to a Demigod Civil War conflict between the two groups back during the American Civil War, after which the gods manipulated the Mist as tightly as possible to stop the two groups from ever meeting each other again, although there have been some close calls. The head of their camp is an immortal she-wolf, Lupa, who originally cared for Remus and Romulus, the demigod sons of Mars Ultor and founder of Rome.
Demigods have ADHD (though it varies between demigods), which hard-wires them for battle, and dyslexia, which they have because their brains are hardwired for Ancient Greek or Latin. Demigods are the only mortal beings who can (partially) see a god's divine form without being destroyed because of the ichor in their blood keeping them alive. Demigods inherit some control over their divine parent's domain, such as Pesra's ability to manipulate water. Some demigods also show some control of magic, like when they summon monsters. Demigods also have a wide variety of other abilities that they all share, but these abilities vary depending on godly parent, including superhuman strength, speed, superhuman senses, agility,above-average healing-factor, durability, endurance, etc.