A wizard is a kind of magician. A wise man who can perform magic spells in a fairy tale or fantasy novel is often described as a wizard.
One of the most famous fictional wizards is Harry Potter, who first learns of his magical abilities when Hagrid says, "Harry — yer a wizard." Sometimes wizards are described as male versions of witches, while other stories use the term as a gender-neutral name for anyone with magical powers. Colloquially, you might call someone a wizard if they're truly amazing at what they do (even if it's not magic): "She's a wizard at dog training!"