This scene is often used to illustrate an early Communion.
It comes from the Via Labicana catacombs near the Church of Saints Marcellus and Peter in Rome. The church itself is fourth century in origin; see here, for the architectural context of the scene within the catacomb.
More specifically illustrates an Agape Feast ("love feast" - as the inscription states: Agape da calda/Irene misce [mi]), described by Pliny to Trajan in a letter detailing his persecution of Christians (97.66):
"they met on a stated day before it was light, and addressed a form of prayer to Christ ... after which it was their custom to separate,and then reassemble, to eat in common a harmless meal."
The practise apparently died out quite early on, and by the third century Communion was generally no longer followed by a communal meal.
One reason may be that these events often turned a little too rowdy, according to St. Augustine [Letter 22 to Bishop Aurelius, 1.3], due to a little too much wine ....
Nowadays not only does one not have wine with a post-Communion meal, but one very rarely has wine at Communion in a Catholic church. And in some rare instances - such as Douglas Kmiec, because he endorsed Obama - one don't even get the remaining bread bit of Communion.