TBT is an acronym which stands for 'Throwback Thursday.' This slang is often used on social networks as a hashtag (#TBT). #TBT is used to reference a moment in the past, for instance, if someone is posting a picture from the past they caption it with #TBT. As time passed TBT's meaning has changed to Throwback To, this is because many of the references are not on a Thursday.
Another definition for TBT is Truth Be Told, it's often used in online chats when someone is about to make an opinion. For instance, after listening to a whack song online, someone might said "TBT, only raccoons will like this song, cause we all know how much they love garbage." This meaning is sometimes used instead of To Be Honest (TBH).