The story
Abbiocco is the heavy drowsiness that comes over you after a big meal. Italian made the noun from the verb abbioccarsi, and the verb tells the story. It is said of a hen settling down to brood and curling up on her eggs, and also simply means to doze off. Someone with an abbiocco sinks down like a broody hen on her nest.
The set phrase is 'mi è venuto l'abbiocco', literally 'the abbiocco has come to me'. You do not do it; it happens to you. The Treccani dictionary labels the word regional and defines it as the temptation to fall asleep.
English has 'food coma', a recent and slightly alarmed coinage, and in American slang 'the itis'. Doctors call it postprandial somnolence. All three treat it as a problem to be solved with coffee. Abbiocco sounds more like a fixed part of the afternoon, the moment the chair edges back from the table.
A scene: a Sunday in August, a long table in the shade. After a plate of fettuccine and a piece of roast lamb, the conversation thins out. Grandfather's chin sinks slowly towards his chest, a cousin stares at the tablecloth, and the youngest children are already asleep under the olive tree. Nobody suggests clearing up. Someone says only, half yawning, 'Che abbiocco.'