As a Spaniard that has visited Italy, I can attest that they definitely understand us and we understand them, at least for the basics. However, there are interesting differences, like the way we pluralize words (quite different in both languages) or the lack of certain prefixes that Spanish imported during the Arabic occupation (carciofo -> alcachofa, zucchero -> azúcar, etc). I haven't studied Italian but I guess that the grammar is very similar.

It's a little like Galician or Catalonian (languages without an army or navy ;) ), the other latin languages spoken in Spain (then there is Basque, but that's a completely different thing): they have palpable differences to Spanish, but in most cases both tongues can reasonably understand each other without many problems (it also helps that most Galician and Catalonian speakers also speak Spanish, of course).