1. They promise that if you get sued for using something open source that Azure is built on, they will indemnify you. Eg, with AWS, in theory someone could say to you: "We have a patent on DB replication, you use MySQL with RDS, that has replication, you owe us money." Unsure if that's a valid risk, but maybe.
2. If you get sued and you've been paying $1k a month or more to Azure, MS will give you one of a their 10k patents on a list if it'll help mount a defense. Could be helpful, I suppose, but hard to figure out the value. If I'm sued, AND MS has a relevant patent on the list, how useful would it be?
3. MS promises that IF they transfer some of their patents to a patent troll in the future, the terms of the transfer will prevent the troll going after you. Again, hard to quantify the value, especially since it depends on MS's actions. "We have a big hammer, but we promise not to hit you" is only partially reassuring. But still better than no promise at all!
On balance these all seem like unmitigated goods, although it's hard for me to evaluate if they have any value. It never occurred to me to be concerned that I might be sued for using open source tools on AWS. :)
I'd estimate it to be about 80% marketing, and 20% a good faith attempt at defusing the disaster that is modern IP laws.
(Edit: And contrary to some other commenters, I don't see anything malicious or harmful going on here.)