Tacitus wrote the Annals in the early second century, covering the reigns from Tiberius to Nero. His account of the great fire at Rome in 64 CE reports that Nero fastened the blame on a group the populace called Christians, and explains the name by reference to Christus, executed under the procurator Pontius Pilate in the reign of Tiberius.
Why it matters, precisely
It is a hostile witness. Tacitus describes the movement in contemptuous terms and shows no interest in defending it. That is what makes the passage evidentially useful: he had no reason to invent the detail he supplies, and he supplies it in passing while explaining something else.
What it attests is narrow and real: that by the early second century a Roman senatorial historian could state, as background, that the movement’s founder had been executed by a named Roman official under a named emperor.
The disputes, which should not be hidden
The passage survives in a single principal manuscript line, and its authenticity has been questioned, though the mainstream position accepts it. Tacitus uses the term procurator for Pilate, whereas the Pilate inscription found at Caesarea gives the title prefect — most read this as Tacitus using the title current in his own day rather than as an error of substance. And Tacitus is writing some fifty years after the fire and eighty after the execution; he is a witness to what was known and said in his time, not to the event.
How it is cited here
By Internet Archive identifier, which resolves to the item record and returns the title. The Church and Brodribb translation is out of copyright and readable in full.