Arabella Figg is a character in the Harry Potter book series by J.K. Rowling.
Massive SPOILERS from Harry Potter and the Order of the Phoenix ahead!!!
We are first introduced to Arabella as "Mrs. Figg", one of the Dursleys' neighbor. Harry Potter, the Dursleys' adopted child is every year left at her house while Dudley Dursley goes somewhere with his parents and a friend for his birthday.
In 1991, It's Dudley's birthday again, and he is going to the zoo with a friend, Piers Polkiss. Mrs. Figg has a broken leg, and Harry can't stay at her house. Harry is extremely happy. He really hates Mrs. Figg's cat-full cabbage-smelling house.
In this stage it is assumed that Figg is a muggle - a non-wizard person, and Harry hates her.
In the end of book 4, after Lord Voldemort's rebirth (1995), Albus Dumbledore tells Sirius Black to alert several people, including Arbella Figg.
In interviews after book 4 was published, Rowling stated that Arbella Figg is indeed Mrs. Figg. In this stage, most fans assumed Figg is a witch.
In the beginning of book 5 we learn Mrs. Figg is actually a squib - a person from a wizarding family who can't do magic. She was directed by Dumbledore to keep an eye on Harry at the Dursleys'.
We also learn that the group of people Dumbledore recruited is called "the Order of the Phoenix", and that Arabella Figg is one of the members in it. The Order of the Phoenix is a group of people (mostly witches and wizards) who fight Voldemort and the Death Eaters.