I was wondering this yesterday too. My husband asked if the watch would work if he was out mowing the lawn (and left his phone inside). I wasn't sure what to tell him... what will work and what won't work? I assume the time, at the least, will work. Other than that, I'm thinking that it will be like being in airplane mode. You can access the apps that don't need to go online and won't get any notifications.
Will photos, music, etc be downloadable for "offline" access? If so, they didn't mention a storage capacity did they?