Biblical scholars agree that Jesus of Nazareth, a Jewish man from a working-class background in Judea, would have spoken Aramaic, a 3,000-year-old language that shares linguistic DNA with Hebrew.
The New Testament, which records the life and works of Jesus, was first written in Greek, but snippets of Aramaic survive in the text. In Mark 5:41, for example, Jesus raises a child (Jairus' daughter) from the dead, saying "Talitha cumi," which is Aramaic for "Little girl, I say to you, arise!" And in Matthew 27:46, Jesus cries out in agony from the cross, saying, "Eli, Eli, lama sabachthani?," meaning "My God, my God, why have you forsaken me?" in Aramaic.
Several languages were spoken in Jesus' time (first century C.E.), when the Roman Empire ruled Judea, a Jewish kingdom. Aramaic was the "everyday" language of conversation and commerce among Jews like Jesus and his followers. That's why most of the Aramaic words and phrases in the New Testament are direct quotes attributed to Jesus.
Jesus may have also understood and spoken some Greek, too. That's because Greek was the lingua franca of the Roman world and was spoken by traders who plied their goods throughout the ancient Mediterranean. Latin, meanwhile, was reserved for legal and military matters, so Jesus probably knew little if any Latin.
What about Hebrew? The Torah and most of the other books of the Hebrew Bible (known to Christians as the Old Testament) were originally written in Hebrew, although there are fragments of Aramaic here and there (Genesis 31:47, for example). The two languages do have some commonalities, but also many differences.
In Jesus' time, Hebrew was mostly read and written by religious scholars and scribal elites. Jesus may have been able to quote the scriptures in Hebrew from memory, but as a member of the craftsman class it's unlikely that he could actually read and write in Hebrew or any other language.
Aramaic is an ancient Semitic tongue that originated with the Aramaeans, who lived in the northern part of modern-day Syria. Aramaic was once spoken across the Middle East, carried by conquering armies of Assyrians and Persians into new territories. Most of the speakers were Christians and Jews in the Middle East who dispersed to other regions because of persecution and took up other languages.
Over the millennia, Aramaic splintered into 150 dialects and is still spoken today by pockets of Christians and Jews living in Iraq, Syria and Eastern Europe, although the modern tongue would be unrecognizable to Jesus.