"I am hungry."
It's also the same in French j'ai fame not je suis fame. It's because in these languages the literal translation is "hunger", i.e. the word is a noun, whereas in English we use an adjective (hungry) - so you "are" and adjective and you "have" a noun.
Neither is right or wrong, they just reflect a different way of looking at the world.
Ho fame = I am hungry Ha fame = he/she/it is hungry. They both mean 'have,' but they are both different conjugations. Ho is I have, Ha is he/she/it has, Hai is you have, Hanno is they have, Avete is you (all) have, and Abbiamo is we have. If you are just beginning, the next time you have to translate from English to Italian, hover over the verb and it should give you a word with a big C by it. Click on it. It will give you the conjugation of the verb. They almost always end the same; -o, -i, -no, -te, -iamo.