Jesus is mentioned in several historical texts outside the Bible. The most commented on is Josephus (Antiquities of the Jews 18.63-64).
Now there was about this time Jesus, a wise man, if it be lawful to call him a man; for he was a doer of wonderful works, a teacher of such men as receive the truth with pleasure. He drew over to him both many of the Jews and many of the Gentiles. He was [the] Christ. And when Pilate, at the suggestion of the principal men amongst us, had condemned him to the cross, those that loved him at the first did not forsake him; for he appeared to them alive again the third day; as the divine prophets had foretold these and ten thousand other wonderful things concerning him. And the tribe of Christians, so named from him, are not extinct at this day.
Some scholars doubt the authenticity of this passage because it is a little too emphatic about Jesus being the Christ — would a devoted Jew like Josephus really say “he was the Christ”? Different scholars have proposed different wordings for the “original” passage — most accept that the original probably said something about Jesus, though some doubt it.
If this was the only testimony about Jesus then the skeptics might have a case, but there are others. For instance, Josephus talks about Jesus in another passage (Antiquities of the Jews 20.9).
… therefore, Ananus was of this disposition, he thought he had now a proper opportunity. Festus was now dead, and Albinus was but upon the road; so he assembled the sanhedrin of judges, and brought before them the brother of Jesus, who was called Christ, whose name was James, and some others; and when he had formed an accusation against them as breakers of the law, he delivered them to be stoned …
The authenticity of this passage is not doubted. Not only does it confirm that Jesus existed, but also confirms that he was called “Christ” by his followers.
Two Roman historians also mention Jesus:
Consequently, to get rid of the report, Nero fastened the guilt and inflicted the most exquisite tortures on a class hated for their abominations, called Christians by the populace. Christus, from whom the name had its origin, suffered the extreme penalty during the reign of Tiberius at the hands of one of our procurators, Pontius Pilatus, and a most mischievous superstition, thus checked for the moment, again broke out not only in Judaea, the first source of the evil, but even in Rome, where all things hideous and shameful from every part of the world find their centre and become popular. Accordingly, an arrest was first made of all who pleaded guilty; then, upon their information, an immense multitude was convicted, not so much of the crime of firing the city, as of hatred against mankind. Mockery of every sort was added to their deaths. Covered with the skins of beasts, they were torn by dogs and perished, or were nailed to crosses, or were doomed to the flames and burnt, to serve as a nightly illumination, when daylight had expired.
Tacitus, Annals 15.44
As the Jews were making constant disturbances at the instigation of Chrestus, he [ Claudius ] expelled them [the Jews] from Rome
Both these historians misspell “Christ” — not surprising given it was an unfamiliar term to Romans at the time — but there is no question in their minds that this Christ was a real person. There are other passages that mention Jesus as a real historical figure which are discussed here.
Lastly, it is worth pointing out that whilst the Bible is a religious text it is also an invaluable historical source because these are geniune texts written within living memory of the time of Jesus.