Arabella Figg most commonly known as 'Mrs Figg' was an elderly squib who worked for Albus Dumbledore as a member of The Order of the Phoenix. Her main task given to her was to keep an eye on Harry Potter as he grew up on Privet Drive with Petunia Dursley and Vernon Dursley, his aunt and uncle respectively. Growing up, Harry thought of Mrs Figg as a "his batty old cat-obsessed neighbour" and never knew her relation to the Wizarding World.
 Character development
Living as a squib in Little Whinging, which was near the Dursley Home, Dumbledore asked Mrs Figg to look over Harry Potter as he grew up with the Dursleys. Her duties included making sure of the safety and well being of Harry Potter and protecting him from Lord Voldemort, reporting any problems she faced. At least once a year, Harry would have to stay with Mrs Figg who had various cats which Harry would have to play with as well as look at photos of all the cats Mrs Figg had even owned. 
 Philosopher's Stone
Mrs Figg was first mentioned after she couldn't look after Harry on Dudley Dursley's birthday. Unfortunately for Dudley, Harry ended up going to the zoo with Dudley and his friend Piers after all as they couldn't find someone else to look after Harry. 
 Order of the Phoenix
In 1995, Mundungus Fletcher, a fellow Order member, was meant to be watching the Dursley Home though instead apparated elsewhere. As he is not watching, Harry Potter goes out for a walk and runs into Dudley Dursley. The pair of them are later attacked by Dementors, and sensing them, Mrs Figg finds them on the ground from the attack. As she brings them back to their house, she tells Harry that she is actually a squib and information on her mission from Dumbledore. She also reveals that all the years that she seemed to be a sarcastic, cranky old lady, she was really just trying to hide her real idenity. Once she finds out that Mundungus left his spot, she is extremely angry, even threatening to hit him.  Mrs Figg is later called on for Harry's trial, after he illegally used a Patronus Charm in the presence of a muggle. At first, Mrs Figg's description of the dementors isn't convincing, but by describing the effect the dementors had on her, most of the Wizengomot believed her story. Eventually, because of Mrs Figg's testimony, Harry was cleared of all charges. 
 Half Blood Prince
After the death of Albus Dumbledore in 1997, Mrs Figg attended his funeral at the white tomb on the lake.
 Portrayals within films
Arabella Figg was portrayed by Kathryn Hunter in the film adaption of Harry Potter and the Order of the Pheonix.
 Outward appearance
Mrs Figg is described as an eldery woman with grizzled grey hair. She often wears old worn clothing and tartan slippers.
As Harry grew up with Mrs Figg she was shown to be a sarcastic and insulting woman who Harry didn't really like. She often forced Harry to look at photos of all her old cats, which Harry hated as he was always bored. Although she was the only non magic member of The Order of the Phoenix, she helped as much as she could, such as watching over a young Harry Potter.
 Accomplishments and skills
Albus Dumbledore approached her for work in The Order of the Pheonix to look after Harry.
As she is Mrs Figg and not Miss, this implies that she is married. Though a husband is never mentioned so she is possibly a widow.