Think of Azure as a server/desktop just not in your office. You can install/setup any programs you want. You have full control over the system except that it's in someone else's building. It definitely comes at a premium. Microsoft Azure/Amazon AWS are top-tier platforms. There are much cheaper ones like OVH that AC uses for things like its Practice Management. If a smaller practice really wanted to be in the cloud, I would probably recommend OVH.

Azure depends on the Internet like any cloud service. One cool feature is that Azure Site Recovery that Microsoft has made reasonably affordable for practices that need a fully functioning secondary backup server. Continuous replication at specified intervals. But your current network and infrastructure have to be designed properly from the ground up for that failover to work properly. It's great thing for larger practices. (Assuming they have the bandwidth for it.)