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.