The Carboniferous was a Period of Earth history.
When a Fire-God entered the Doctor's TARDIS, it persuaded the TARDIS to go back in time to the "dawn of Earth" to experience the "pure elemental powers of creation." The TARDIS sank in the mud but returned to Wells Wood in response to bulti-in safety features. Observing the corals of the limestone, the Fifth Doctor dated the limestone to the Carboniferous Period, or around 500,000,000 BC. The impression of the TARDIS in the limestone was unearthed by quarry workers in the 1980s. (COMIC: The Stockbridge Horror)
Behind the scene
In actuality, the Carboniferous is 60,000,000 to 358,900,000 years ago. 500,000,000 years ago is in the Cambrian.