Pretty much TBT is the currency used on the forum to buy collectibles, customize your profile, and complete actions like starting groups. You can earn it by posting regularly on the forum. Because of this, many people desire TBT and will trade you Bells or in-game items for it.
Ive seen 100 TBT go for somewhere between 1.5 and 2.5 million in-game Bells.
Depends on exactly what you are buying with your TBT.
Let's take my profile for example. If you look underneath my profile pic and name, you will see a pear and an emerald. These are called collectibles. They are exclusively found within the forum and will not affect your game whatsoever. If you wanted to buy one of these, you would tell the person selling, transfer the TBT, and they will transfer the collectible to your account.
However, if you go to the forum on the mainpage called "TBT Marketplace", you may find vendors selling furniture sets, hybrids or even exchanging Bells for TBT. All of these are in-game items you would either have to pick up or open your gate for. If you wanted to, say, sell 100 of your TBT for 1.8 Million Bells, you would transfer the Bells and add their Friend Code. Then you would either go to their town or have them come to yours (depending on what you agree upon), where they will drop off the Bells for you.