No-one knows the exact etymology (origin of the word) for "Italia". However, the historian Dionysius of Halicarnassus reports two possible origins (see section 35 here):

1. There was a great king of the Oenotrians (early inhabitants of southern Italy) called Italus, who eventually gave his name to his people.

2. Dionysius tells a story about Hercules and a calf; while this is probably made up, the important thing is that one of the words for "calf" in Greek - which was the predominant language of southern Italy centuries before Latin became dominant - is italos. Bulls were symbols of the Southern tribes of Italy - the region originally known as "Italia" - which would suggest that the name means something like "land of the calves".