Tabgha, a corruption of the Greek word 'heptapegon' (seven springs), is the place where seven streams meet. On the edge of the Sea of Galilee this is a useful watery confluence, but also a deeply spiritual site, given its place in the ministry of Jesus. There has been a shrine here since around AD 350, when Joseph of Tiberias founded one. With Byzantine, Crusader, and Ottoman interest and influence, it's a place which both takes you in Jesus' footsteps and reminds you of the long history and tradition those footsteps founded.
The miracle of the feeding of the five thousand is said to have taken place here, and is commemorated by the mosaics inside the church (see for example Matthew 14:13-21 or Mark 6:34-44). Laid next to a rock, it has even been suggested that this is the very spot of the miracle.
The church - bread and fish mosaic in front of the altar
The mosaics are splendid in general. They're well preserved, in fact, successive rebuildings of the church have led to awkward architectural alignments in order to keep them visible. Details such as the peacock, a symbol of immortality, remind us of the allegorical nature of much Christian teaching, including parables possibly even told in this very place.
On a larger scale, they're impressive. This site is also said to be the place of Jesus' fourth appearance to his disciples after his resurrection, and it is appropriate for the place to be marked in some strong way. The church itself displays the simplicity one would expect from the Benedictines who mind it, but this lends a elegance and simple beauty to the place. Unusually, the church falls under the control of the German Association of the Holy Land.
Useful information signs are placed around the site, detailing the life of Jesus as relevant to this place, or focussing specifically on the miracles. There has been some kind of shrine here since the fourth century, so the layers of interpretation needed run deep.
Further up the hill is the supposed site of the Sermon on the Mount, where Jesus preached the Beatitudes themselves, as well as the Church of the Primacy of St Peter. If you have time, it's worth wandering around the site at large. The natural setting is beautiful, and you can find spots for excellent views of the Sea of Galilee. Just a few minutes from the much better-known site at Capernaum, this is a remarkable spot, well worth stopping at, if only for half an hour.
There is limited parking, which can easily become blocked by the large volume of coach traffic. There are limited other facilities, including a small shop. You are best driving here, staying somewhere like Nazareth (c.40 minutes away) or Tiberias (c.20 minutes away).