Tabgha is the location of a pair of sites traditionally associated with Jesus and fish. The name is likely a corruption of the Greek name, Heptaegon (Seven Springs).
The first site is the Church of the Primacy of St. Peter, the traditional location where Jesus after his resurrection appeared to the apostle Peter and caused a miraculous catch of fish. Jesus asked Peter three times if he loved him (Matthew 16) and Jesus' commandment to feed his sheep is cited as the start of the Catholic tradition of Peter's leadership of the church that has continued through the succession of Popes.
The second site is the Church of the Multiplication, a German Benedictine Church from 1936 built over a flat rock called the Mensa Christi (Table of Christ) that is the traditional location of Jesus' miraculous feeding of 5,000 men with only five loaves of bread and two fish (Matthew 14).
My mother echoed the skeptical sentiments of many in the group in remarking that, "That rock had nothing to do with Jesus."