A T-bucket is a specific style of hot rod

Hot rod

Hot rods are typically American cars with large engines modified for linear speed. The origin of the term "hot rod" is unclear. One explanation is that the term is a contraction of "hot roadster," meaning a roadster that was modified for speed. Another possible origin includes modifications to or...

 car

Automobile

An automobile, autocar, motor car or car is a wheeled motor vehicle used for transporting passengers, which also carries its own engine or motor...

, based on a Ford Model T

Ford Model T

The Ford Model T is an automobile that was produced by Henry Ford's Ford Motor Company from September 1908 to May 1927...

, but extensively modified, or alternatively built with replica components to resemble a Model T.
Since the last Model T was built over eighty years ago in 1927, modern T-buckets are generally replicas as there are few real Model Ts left in scrapyards to build upon.

A genuine T-bucket has the very small and light two seater body of a Model T roadster (with or without the turtle deck or small pickup box), this "bucket"-shaped bodyshell giving the cars their name.