Capernaum (Kfar Nahum in Hebrew) is located on the northern end of the Kinneret Sea. It was apparently founded during the Hasmonean period, around 150 BCE, as a fishing and agricultural village. It grew during the Roman Empire and was inhabited until the beginning of the Muslim period in the 8th century.
The Besorot mention that Yeshua centered his teaching from this little town, possibly because of its easy access to the water and because some of his talmidim lived there. Specifically, we know that Kefa and his family lived in Capernaum and that Yeshua healed Kefa's mother-in-law there (Matthew 8:14-17). Yeshua also healed other people in Capernaum, including the woman with the issue of blood (Matthew 9:20-22); Jarius' daughter, who he brought back from the dead (Matthew 9:18-26); and the man who had the withered hand, who Yeshua healed on Shabbat (Matthew 12:9-14). The first century Synagogue (made of black basalt stones) in Capernaum was constructed by the Roman centurion who was in charge of the garrison in the city somewhere around 20 CE. Yeshua taught in this synagogue (Mark 1:21) on more than one occasion, and in one famous drash he refered to himself as "the bread of life." (John 6:30-59)
The first century synagogue was destroyed during the First Jewish Revolt in 70 CE, and another, more extensive and beautiful synagogue was built on top of the remains during the third century. The city was a center for Messianic Jews for many centuries (See Nazarene Jewish Christianity: From the End of the New Testament Period Until Its Disappearance in the Fourth Century. (Jerusalem, Israel: The Magnes Press, The Hebrew University), 102-3), until the Council of Nicea made Jewish practices illegal.
Link: Jewish Virtual Library.
Link: Capharnaum, official website of the Franciscans who run the site.
