Wizards (male) and Witches (female) are terms for a human who are born with the ability to use and manipulate magic. This ability is an inherited trait passed from parent to child. While pure-bloods are born of two wizarding parents and half-blood sare often born of one wizard and one muggle or muggle-born parent, Muggle-born wizards and witches are born with their magical abilities because they are distantly descended from a Squib who often marries into a Muggle family. From this point on, that branch of the wizarding family often loses all traces of its wizarding legacy, which resurfaces many generations later in a Muggle-born descendent.
In childhood, wizards and witches may exhibit random bursts of magic, called accidental magic, which are honed and controlled as they progress in maturity. To perform controlled magic, almost all wizards/witches need to use a wand, although the skill of without a wand may be mastered in later life. A few highly advanced wizards can do controlled magical acts without a wand, such as Albus Dumbledore, who demonstrated the ability at the close of Harry Potter's first year at Hogwarts School of Witchcraft and Wizardry, and Lord Voldemort, who once demonstrated this ability during the Battle over Little Whinging in 1997.
Magical Skills and Abilities
Seers
Some wizards are born with abilities beyond those of the average wizard. Seers, for example, have the skill of insight into future events. They may garner this insight through visions and dreams or through scrying physical objects like tea dregs, tarot cards, and crystal balls.
Animagi
While some wizards have the ability to turn into animals, it is not an inherent power, but rather a trained technique. This type of wizard is called an Animagus (plural Animagi). Babbitty Rabbitty was said to be an Animagus with the ability to transform into a rabbit. Sirius Black was an Animagus who could turn into a black dog named Padfoot. Rita Skeeter is an Animagus who can turn into a beetle and used this for gathering information for her articles. James Potter was an Animagus who could turn into a stag. Peter Pettigrew was an Animagus who could turn into a rat. He masqueraded as "Scabbers," Ron Weasley's rat, in order to convince the wizarding world that he had been killed by Sirius Black. The Animagi had to register themselves at the Ministry of Magic, because human Transfiguration can go horribly wrong. The first recorded Animagus was Falco Aesalon.
Metamorphmagi
Nymphadora Tonks is a Metamorphmagus, and can change her form at will
Other wizards may have the ability to change only their physical appearance rather than their bodily form. This type of wizard is termed a Metamorphmagus. Such a wizard can change the shape of their noses or hair colour and other physical attributes. Nymphadora Tonks is a known Metamorphmagus.
Communicating with Animals
Some wizards and witches have the ability to talk to animals. For instance, a Parselmouth can speak to snakes. This ability is extremely rare. Other wizards, like Rubeus Hagrid for example, have an innate ability to communicate and bond with all kinds of animals.
Squibs
Individuals from wizarding families who cannot perform magic at all are called Squibs. Squibs are much less common than Muggle-borns.
Arabella Figg is a squib
Occlumens
Some wizards have the ability to protect their minds from others who can perform Legilimency. This ability is called Occlumency.
Severus Snape is both: an accomplished Leglimens as well as an Occlumens
Legilimens
Legilimens are people who can perform Legilimency. These people can tune into other people's minds, but have to work against the people who can perform Occlumency.
Social Habits
As decreed by the International Statute of Wizarding Secrecy, wizards maintain a society entirely separate from Muggle society, with their own culture and traditions. Wizards populate areas all over the globe. At the 1994 Quidditch World Cup, over 100,000 wizards were in attendance. At Hogwarts School of Witchcraft and Wizardry, there are over 600 students in residence at any given time. It is unknown exactly how many witches and wizards are in the entire world, but chances are they are not counted in the six billion population count of Muggles.
Wizards may live together in communities such as Godric's Hollow or Hogsmeade. Other wizards live in solitary locations such as Spinner's End or 12 Grimmauld Place. Most wizards maintain little if no contact with Muggle society and find Muggles strange and unpleasant. Some wizards don't like to talk about their Muggle relatives. Other wizards, like Arthur Weasley, find Muggles to be highly intriguing. Hermione Granger, a Muggle-born witch, took up Muggle Studies at Hogwarts because she felt it would be fascinating to think about Muggles from a wizarding perspective.