I'm a little confused with this one. When does the Italian "per" mean the same as the English "per" and when does it mean "for"?
The English "per" is partitive, and can be usually switched with "for each" (one meal per dog, one meal for each dog): that in Italian can be either "per" or "a" (e.g. un pasto a testa, one meal each).
As with most other prepositions, "per" also introduces many other cases: most of them are the same as "for", but it can also be translated with "around" (e.g. cammino per la città, I walk around town) or "through" (e.g. passa per la finestra, it passes through the window), and so on. It can also express multiplications: three times seven, tre per sette.