The Flea Market is a weekend event where villagers from the player's town allow others to come in and buy some of their items, although some of their furniture isn't for sale for various reasons. Many animals choose to sell items at a raised amount.
The player can also sell his/her own belongings - any furniture out on the ground floor when villagers visit is up for sale. However, even if the player runs out of items to sell, the villager will take a few minutes to leave unless the player leaves the house, and in the event the player will return to his or her home. If the player leaves and re-enters their house enough, every villager that is outside will come in once, with other villagers being available to enter your home when they have left their own, on a certain hour.
Items or creatures that a villager buys from the player's house usually will be displayed in their house the next day.
Flea Markets are held usually on Sundays (except in Wild World, where they are held on Saturdays) but if the player is ahead of a scheduled Flea Market (due to a time-warp), then time-warps back in time, the Flea Market will be set to the next day (like a lot of other events).
When the player is buying from villagers, the player can either take the price they give you, or leave it. If one of them is buying from the player however, they will haggle by saying the price is too high, and the player will have to lower it for them to buy it.
A villager will buy a max of three items from the player's house. However, if the player goes into a different room without leaving the house, then go back to where the villager is, it resets it so that the villager will buy another three items. This can be repeated indefinitely. The maximum acceptable price they will pay is a little over twice the selling price to Tom Nook, which means for furniture, they will sell for half the buying cost. If the player has bugs or insects in your house, the same rule applies, twice the selling price. So if the player stocks up on high priced fish/insects before or during a flea market day, the player can make double amount of bells by placing them in their home and coaxing the villagers towards the creature.
If the player turns off the lights, the villagers will not know you are home, so the player can move around furniture to prepare, as you cannot when you have a visitor.
Flea Market is not present in Animal Crossing: New Leaf. It is because Re-Tail acts like a Flea Market as villagers and the player can place items there where anyone will buy them including the villagers themselves and any friend visiting your town.