Unless your moving company provides your moving storage, you're entirely responsible for your belongings when they're stored away. Even if all the responsibility isn't yours, it's a good idea to check into the possibility of obtaining storage insurance for your valuables.
Take a complete inventory of your items before you place them into moving storage, because it's your responsibility to keep track of them. The inventory will come in handy in case you need to make any insurance claims, or if something comes up missing.