Flea Bottom is the poorest slum district in King's Landing, located on the western side of Rhaenys' Hill. It is a maze-like warren of narrow streets, ramshackle buildings, and dark alleys.
Ser Davos Seaworth was born in Flea Bottom, the son of a poor crabber, but escaped that harsh life as soon as he could by becoming a smuggler. Gendry was born to a tavern wench in Flea Bottom and spent much of his childhood there, which was made even harder after his mother died when he was very young. When royal agents discovered that he was secretly a bastard son of King Robert Baratheon, however, it was decided to look after the boy's well-being by secretly arranging for him to work as a blacksmith's apprentice for Tobho Mott. Gendry was happy to leave Flea Bottom, moving to the better district of the city near Tobho Mott's armory on the Street of Steel.
Arya Stark takes refuge in Flea Bottom after fleeing the Red Keep. She kills a pigeon in the Street of Flour where the bakers ply their trade, as birds are attracted to the crumbs. When she tries to barter it to a baker for bread, he refuses. Arya is in Flea Bottom when she hears the crowd say her father is being taken to the Sept of Baelor.
While talking to Daisy, a new prostitute in Petyr Baelish's brothel, Ros identifies Armeca as being from Flea Bottom, but notes that she likes to pretend she is from more exotic climes and doesn't speak the Common Tongue of Westeros.
As the royal family is returning from the docks where they saw off Princess Myrcella Baratheon for her voyage to Dorne, the starving smallfolk of the city hurl insults at Joffrey, and ultimately someone hurls cow excrement in his face. Joffrey brashly shouts for his guards to "kill them all!", sparking off a city-wide riot. Flea Bottom is badly affected by the food riots.
Lady Margaery Tyrell stops in Flea Bottom unexpectedly to visit an orphanage and interact with the children. Her servants pass out bread and toys, earning her the love of Flea Bottom's Smallfolk. That evening, Joffrey and Cersei visit Margaery and her brother Loras Tyrell, for a small dinner party. Cersei admonishes Margaery's boldness and reminds her that her impromptu charity work took place on the same streets where the royal party was assaulted weeks earlier.
Behind the scenes
In the books
In the A Song of Ice and Fire novels, Flea Bottom was the home of the famous knight Ser Duncan the Tall, who ended up as Lord Commander of the Kingsguard. Davos Seaworth also grew up in Flea Bottom, the son of a poor crabber. He left as soon as he could by becoming a smuggler operating in Blackwater Bay and the Narrow Sea. The books do state that Gendry was born to a tavern girl in King's Landing, though they haven't specified that he lived in Flea Bottom before he came to work for Tobho Mott.
It is a dismal and disreputable place. The alleys are narrow and buildings lean toward each other. King's Landing was rapidly constructed within the first century of rule by the Targaryen dynasty, to serve as a capital city for their new unified realm. This rapid expansion didn't keep pace with organized "city-planning", resulting in numerous slums, of which Flea Bottom is the worst. Many of these slum districts are poorly organized, ugly, and filthy because their placement wasn't thought out during the rush to slap down new buildings. In contrast, the second largest city in Westeros, Oldtown in the Reach, is thousands of years old, but grew only in incremental steps which were well planned out beforehand, resulting in it being a much better organized and beautiful city without the squalid slums of King's Landing, while being only slightly smaller than the capital itself.
Survival on the streets of Flea Bottom is tough and hardening. The district is full of tanneries (which make the air stink), cheap brothels, low-class inns, winesinks, and pot-shops serving meager bowls of brown. Arya finds an establishment in Flea Bottom where she can take a pigeon and get half of it back cooked, in exchange for the other half. Before that she had to eat it raw. When Arya left the Red Keep she took a bundle of clothes and things to sell, but they were stolen the first night she slept in Flea Bottom (she was sleeping on top of Needle or would have lost it too).
A large part of Flea Bottom burns down the night following Joffrey's riot.