According to the apostle John, before the Crucifixion, and after Jesus had been dressed in a purple robe and a crown of thorns, Pontius Pilate declared, "Behold the man."1 Ecce Homo is Latin for "Behold the man," and the Ecce Homo Arch, according to a tradition dating at least from the time of the Crusades, is at the place where this occurred.
The Ecce Homo Arch itself, a Roman triple arch, didn't exist during the life of Jesus, and is tentatively dated from the second century A.D.2
Jack Finegan, in Light From the Ancient Past, presents corroborative evidence that this traditional site is the correct one. Finegan points out that the the traditional location of the trial, the Antonia Fortress, a large castle-like structure which was located near the beginning of the Via Dolorosa, has been partially excavated, and contains slabs of stone that could be relics of the area called "the Pavement" by the apostle John, where Pilate sat in judgement.3,4
1 The Bible, King James Version, John 19:5
2 Herbert G. May, Editor, Oxford Bible Atlas, (Oxford, U.K.: Oxford University Press, 1984), 97
Information about the geography of Jerusalem during the lifetime of Jesus is scant, and there isn't a unanimous opinion that the traditional location of the trial of Jesus is necessarily correct. The Oxford Bible Atlas, for example, argues that the trial of Jesus took place at the palace built by Herod - the present site of the Tower of David.
3 Jack Finegan, Light From the Ancient Past , (Princeton, NJ: Princeton University Press, 1959), 320-321
4 The Bible, King James Version, John 19:13
1Then Pilate therefore took Jesus, and scourged him. 2And the soldiers platted a crown of thorns, and put it on his head, and they put on him a purple robe, 3And said, Hail, King of the Jews! and they smote him with their hands. 4Pilate therefore went forth again, and saith unto them, "Behold, I bring him forth to you, that ye may know that I find no fault in him." 5Then came Jesus forth, wearing the crown of thorns, and the purple robe. And Pilate saith unto them, "Behold the man!" 6When the chief priests therefore and officers saw him, they cried out, saying, "Crucify him, crucify him." Pilate saith unto them, "Take ye him, and crucify him: for I find no fault in him."
The Bible, King James version, John 19:1-6