We've known about Mrs. Figg since Book 1, when we find out that she is an elderly woman living near the Dursleys who loves cats and sometimes babysits Harry. She just seems like a one-off joke character. But then, in Book 5, we find out that there is a lot more to Mrs. Figg than it first appears. She is a Squib, which means that her parents were magical but she is not. However, she is familiar with the wizarding world. She also works with Professor Dumbledore: she has been watching Harry on Dumbledore's behalf since he first came to live with the Dursleys fourteen years ago.
Mrs. Figg witnesses the dementor attack on Harry and Dudley at the outset of the novel. She becomes a material witness for Harry at his hearing for the underage use of magic. Since she is a Squib, she couldn't help him battle the dementors herself (in fact, there are even hints that she can't see them physically), but she does give an excellent description of what the dementors are like:
I felt them. Everything went cold, and this was a very warm summer's night, mark you. And I felt ... as though all happiness had gone from the world ... and I remembered dreadful things. (8.52)
With this evidence, the Wizengamot accepts that there were dementors in Harry's Muggle suburb and that he had to cast the Patronus spell to protect himself and his cousin, even if he is underage. So Harry gets cleared of all charges.
But while Harry appreciates Mrs. Figg's assistance, her help only adds to his resentment of Dumbledore. He can't understand how he has lived so close to someone who knew about the magical world but never told him for almost his whole life. How could Dumbledore ask someone to guard him and then never tell Harry about it? Mrs. Figg becomes yet another example of Dumbledore's desire to leave Harry out of all of his decisions regarding Harry's life.