Office 365 includes licenses to download the Office programs. You don't have to use any of the cloud features if you don't want to. But there's a ton of useful stuff in there.
Yep, the locally installed apps are for offline use. However, they are pushing hard to have your entire Active Directory in the cloud with all of your server infrastructure with Azure. We are currently testing moving our exchange to hosted O365, it’s been a huge process and a little scary.