Zach Stagers has an introductory post to Azure Notebooks:
No installation, no maintenance
As with any PaaS solution, Azure Notebooks makes it far quicker and easier to get up and running, as there’s no download or installation required. Microsoft handles all the maintenance for you too!
I’m working on a fairly big project using Azure Notebooks. It’s very helpful getting 1GB of space, so I can include all of my data, images, etc. from a fairly large number of notebooks. The big downside is that the server running these notebooks is pretty slow—even for a fairly simple ARIMA model, I had it sitting there for 10 minutes at 100% CPU. So don’t expect to run a heavy workload against it.