The physical suffering of Jesus began in the Garden of Gethsemane on the evening before His crucifixion. While the disciples slept, the Gospel of Luke records that the LORD "being in an agony he prayed more earnestly: and his sweat was as it were great drops of blood falling down to the ground."
This was written by the physician Luke, a well-educated man and a careful observer by profession.
Luke is also the only gospel writer to mention the bloody sweat, possibly because of his interest as a physician in this rare physiological phenomenon, which spoke eloquently of the intense spiritual agony Jesus was suffering... (Dr. Henry M. Morris, The Defenders Bible, marginal notes for Luke 22:44)
Although this medical condition is relatively rare, according to Dr. Frederick Zugibe (Chief Medical Examiner of Rockland County, New York) it is well known, and there have been many cases of it. The clinical term is hematohidrosis. "Around the sweat glands, there are multiple blood vessels in a net-like form." Under the pressure of great stress the vessels constrict. Then as the anxiety passes "the blood vessels dilate to the point of rupture. The blood goes into the sweat glands." As the sweat glands are producing a lot of sweat, it pushes the blood to the surface - coming out as droplets of blood mixed with sweat. Jesus wasn't sweating blood because he was afraid of the physical pain of the cross.
Indeed, the book of Hebrews tells us that Jesus looked forward to the cross:
Looking unto Jesus, the author and finisher of our faith, who for the joy that was set before Him endured the cross, despising the shame, and has sat down at the right hand of the throne of God. (Hebrews 12:2)
Taken from "Gethsemane: Where Jesus Prayed for Me!" by Discover the Book Ministries (used by permission).