Witches are humans who possess supernatural powers. They can be male or female (although male witches are better known as warlocks). In folklore, female witches are elderly hags who use dark magic to cause mischief and chaos.
In 1665 (before Dimmsdale was named), Timmy Turner, who had travelled back in time, discovered that Alden Bitterroot was a warlock. Alden was planning to trick the townspeople into naming the town after him.
Alden Bitterroot was able to project his magical abilities through his hands, without the use of a wand or spellbook. Somehow, he was able to block all other kinds of magic (Fairy magic in particular).
He could levitate, project green energy bolts and fly on his broom (like many traditional witches). Alden was able to survive for hundreds of years after falling into a well, possibly through the use of his magical abilities.