The two words together, "da mangiare", can mean "food", constructed with "da" like, for example,
- macchina da scrivere ("machine for writing", typewriter)
- legna da ardere (wood to burn)
- cera da candela (vax for candles)
(Note that similar forms are not always good italian, but are widely used; for example macchina da scrivere is often considered an error, but is much more common than macchina per scrivere).
About da mangiare, the real meaning is "[cosa buona] da mangiare" ("good to eat", or "appropriate to be eaten"), like legna da ardere which means "wood good for burning".
The following phrases can be seen normally:
- compro da mangiare (I buy food)
- serve da mangiare (food is needed)
- siamo senza roba da mangiare (we have no food)
- abbiamo niente da mangiare (same)
- siamo senza da mangiare (same; incorrect, but used)
- dagli da mangiare (give some food to him)
Now, "dare da mangiare" has two nuances, "to give food" or "to feed". Probably a farmer feeds his horse, where a wife gives food to her husband (unless he needs assistance).