What does Matthew 27:34 mean?

Matthew provides no detail about the process of the crucifixion itself. Some of that is decency: crucifixion was considered so vile and hateful that it was rarely spoken of directly, or in mixed company. Likely, Matthew's original readers were all too familiar with Roman crucifixion and didn't need Matthew to diagram it for them.

Roman crucifixion was one of the most painful, longest lasting, and shameful ways a person could be killed. It was universally feared by Rome's enemies. It was so terrible that Roman citizens themselves could not be crucified unless specifically ordered to be so by Caesar. It was highly effective in deterring crime and uprisings among the conquered peoples during the time of the Roman empire. The process was at once an act of terror, torture, and cruel precision.

The victim's hands would be nailed to the crossbeam, typically just under the bones of the wrist. In some cases, the palm of the hand would be nailed, but the wrist was a more secure attachment point. Care was taken to pierce nerves and avoid blood vessels, to enhance pain and extend suffering. The crossbeam would then be hoisted onto an upright pole. The feet were nailed in place, using similar care as the hands. The knees would be slightly bent, and the victim's weight would hang entirely on those three points.

This began a slow, excruciating process of suffocation. With outstretched arms being pulled apart, exchanging air in the lungs required the victim to strain against the nails to pull his body up, bringing intense pain. Over time, this became more and more difficult. Eventually, the prisoner simply could not take in any more air and choked to death. Crucifixion victims could linger for hours, or even days, as infection, shock, scavengers, thirst, and blood loss took their toll.

Those dying on the cross would naturally become terribly thirsty. Soldiers would sometimes offer a drink of wine mixed with bitter-tasting myrrh or gall. Scholars speculate this wine mixture was offered as an act of mercy, perhaps by local Jewish women, to dull the pain. Others point to the prophecy in Psalm 69:20–21 to show that there was no comfort on the cross, including in the offer of the wine: "I looked for pity, but there was none, and for comforters, but I found none. They gave me poison for food, and for my thirst they gave me sour wine to drink."

Jesus refused to drink this once he realized what it was. He would be in full control of His mind, and under the full agony of His body, for the entire experience.