In many MMO games, trading is a way to trade items and currency from one player to another. In Guild Wars 2, there is no actual trading window. The closest players can get to traditional "trading" is exchanging items through the mail system, as mail is instant and you can send both items and currency. Trading between characters has to be done through the Bank and Collectible storage systems. One can not mail an item from one of their characters to another one of their characters, unless both characters are on separate accounts.
 Cons to Mail Trading
The problem with trading through the mail is that you can easily get scammed and not get anything in return for an item you have sent. For this reason, there is the Trading Post system, where players can sell their items that they find to other players for in game money. In the first days of the game's release, the Trading post was down for maintenance, forcing players to trade through the mail.
If you do not know the person you plan to mail trade with, you might want to think twice because they could very easily scam you. If you send an item or money first, they could decide not to pay you, and you will have lost the stuff you sent forever. Trading anything more than a rare item is not recommended because it is much worse to lose an Exotic piece of gear than a Rare one, even though both are bad to lose. Mail trading is monitored only by the good old fashioned "Honor System."
 Pros to Mail Trading
If you trade through the mail (Which can be quicker than doing it through the Trading Post), you might be able to make a significantly larger amount of money for your items depending on your world's economy. If you trade through the Trading Post, you will have to go to a main city (or some other locations around the world) and find a Trading Post NPC in order to pick up the money you earned or the item you bought. But if you trade through the mail, the items and money arrive instantly as soon as the other person sends it.
The best time to trade through the mail would be if the Trading Post is down for maintenance, if you have just looted rare gear from a chest that dropped from a group event (as people often like to exchange their rewards for ones they can actually use), and if you know somebody that you want to sell an item to, or just give them an item for free. In other games, you might have to be near a player to trade with them, but in Guild Wars 2, you can trade through the mail and access the Trading Post from anywhere in the game.
 Future of Trading
Trading through a designated trading window system as is used by many other games, was not used by ArenaNet because they wanted to avoid spamming, and other exploits and problems that other MMOs have had. They may implement a new system in the future, but nothing has been said so far. Most people would like to see a new system of trading so they don't always have to rely on the Trading Post or the "honor system" of mail trading.