In humans, magic or the lack thereof is an inborn attribute. It appears to be semi-inherited, as magic is the norm in the children of magical couples and rare in those of Muggles. Exceptions do exist: those unable to do magic who are born to magical parents are known as Squibs, whereas a witch or wizard born to Muggle parents are known as a Muggle-born, or the alternate term "Mudblood". The latter form are far more common than the rare Squibs, but this may be a feature of the disparate sizes of the Muggle and wizarding populations.
Magic exists in a sharply defined moral universe, and magical ability is strongly tied to emotion: spells appear to be good or evil by nature, and the emotions and intentions of the caster affect spellcasting. For instance, according to Bellatrix Lestrange, only one who takes pleasure in the suffering of others can produce an effective Cruciatus Curse; righteous wrath will work, but only to a point. Although it is unknown if this is completely correct as a wizard such as Albus Dumbledore is said to have the powers to do such magic but is too "noble" to use them.
The wizarding society exists as a shadow society to the Muggle world and works as hard as it can to keep its existence a secret, save for all but a few Muggles, such as those who are related to witches and wizards, or important Muggles such as the Prime Minister. To most magical people the Muggle world is unknown, and their attempts to disguise themselves as Muggles often have mostly humorous results. Muggle Studies at Hogwarts is considered a soft option. Most things of magical nature are hidden or otherwise obscured from Muggles; others (such as Dementors) simply cannot be seen by them, but Muggles do feel the effects of them. There is also an office in the Ministry of Magic, for the Misuse of Muggle Artifacts, that deals with people charming objects typically found in a Muggle society, such as the Ford Anglia which Mr. Weasley charmed, or Caractacus Burke's rope that killed eleven people.
The Muggle Prime Minister is first alerted to the existence of the magical 'underworld' on the evening after his election, when the Minister for Magic uses the Floo network to appear in his (or her) fireplace. Thereafter, he is only visited by what the Prime Minister in book 6 called the Other Minister in the event of danger to Muggles, such as the occasion when Sirius Black escaped from Azkaban. On occasions like this, the Prime Minister is given advance notice of the visit by a portrait of an ugly wizard, who tells him. The portrait can never be removed from the wall, at least not by Muggle means.
Spells are the every-purpose tools of a wizard or witch, short bursts of magic used to accomplish single specialised tasks such as opening locks or creating fire. Typically casting requires an incantation, most often in a modified form of Latin and gesturing with a wand. However, these seem to be aids to the will only; wands are in most cases required, but there are indications that sufficiently advanced witches and wizards can perform spells without them. Spells can also be cast non-verbally, but with a wand. This technique is taught in the sixth year of study at Hogwarts and requires the caster to concentrate on the incantation. Some spells (e.g. Levicorpus) are apparently designed to be used non-verbally. While most magic shown in the books requires the caster to use his voice, some does not (and this may depend on the witch or wizard). Albus Dumbledore has been known to do good-sized feats of magic without speaking, such as conjuring enough squashy purple sleeping bags to accommodate the entire school.
It is evidently also possible to use your wand without holding it. Harry himself performs Lumos to light his wand when it is lying on the ground somewhere near him. Additionally, Animagi and Metamorphmagi do not need wands to undergo their transformations.
Spells are divided into rough categories, such as "charms", "curses", "hexes", or "jinxes". Although offensive and potentially dangerous ones exist in number, three are considered to be usable only for great evil, which earns them the special classification of "Unforgivable Curses". The use of these spells on another human being earns a "one-way ticket to Azkaban".