Wizardkind

Wizards (male) and Witchs (female) are the terms used for a human who can use magic, it may sometimes refer to another magic creatures. They are the central characters in the Harry Potter universe.

Magic
By definition, all Wizards and Witchs are able to use magic, a trait that is inereted to the person, and apparently is something that the person is born with. It is unknown (or at least never explained) how people with muggle parents have magical powers, but a theory is that they have distant magic relatives (through squibs).

To peform controled magic, they need a wand, but wizards on situations of great stress are able to peform some magical features without a wand, those situations are rare and the spells rather unstable.

Other powers
Besides "regular" magic, some wizards may have others powers without a wand, these abilities are rare and appear to be concetrated on pure-blood families, they might be result of interbreed with other magical beings, like the case of Fleur who is a part veela and can charm others.

Also there is Animagus, who learn to change in to a specific animal at wil.

List of unusual powers and people who have them:
 * Ability to Entrance- Fleur Delacour and the Veela side of her family.
 * Metamorphmagus - Nymphadora Tonks and Teddy Lupin.
 * Animagus - James Potter, Sirius Black, Peter Pettigrew, Minerva McGonagall and Rita Skeeter.
 * Seer (ability to predict the future) - Sybill Trelawney.
 * Parselmouth (ability to talk to snakes) - Tom Marvolo Riddle and other decendants of Salazar Slytherin. Harry had this ability becuase of his connection to Voldemort.

There is also other abilities that can't be put on the above category, like Hagrid great strenght and size.

Society
By choice, Wizards created a entirely separated society from muggles, they have they own culture and traditions. This apparently happened because the muggle reaction to magic in the middle ages, and since them wizards in the entire world have been hiding.

Despite this, there appears to be very few "pure" wizard cities and places, most of the magical locations are hiding near (or inside) muggle places, like Diagon Alley. Most wizards are show to live in small towns and villages having little contact with the outside world.

As a result of that isolation, Pure-blood Wizards have little knownledge of modern technology or even common muggle culture and habits the examples in the books vary from the inability to understand how muggle money work or that muggle portraits don't move.

Population
It is never truly estabilished how many wizards exist, however the World Cup in 94 was stated to have over 100,000 wizards from all over the world, Hogwarts has something around 1,000 students.

See Blood purity for information on class distinctions between established and new wizarding families