A Bucky is a component of x-ray units that holds the x-ray film cassette and moves the grid during x-ray exposure. The motion keeps the lead strips from being seen on the x-ray picture.
The name refers to Dr. Gustave Bucky who invented the use of filter grids in 1913.

(B) The Bucky factor is the ratio of x-rays arriving at the grid (incident radiation), and those being transmitted through the grid. The Bucky factor describes how much the output of the x-ray tube must be increased in order to compensate for the removal of incident radiation by a grid.
B = incident radiation / transmitted radiation
For example, if for every two x-rays impinging the grid, only one will pass through, then the grid has a Bucky factor of two and the intensity of the x-ray beam must be doubled.