Pretty sure it's verifying SSL certificates of the proxied (backend) servers in a reverse proxy configuration-- so that you know you're talking to the backend server that you think you're talking to (in case your internal network gets MITM'd, I guess, or if you're talking to backend servers across a public network).
At least, that's what I gather from the new config options they linked to (the relevant options are the proxy_ssl_* directives).
Mainline is where new features arrive. Think of it kind of like what used to be Firefox Aurora. Stable is snapshots of mainline taken less frequently that are considered suitable for long term use.
Mainline has newer features, but isn't quite a nightly build. Stable has fewer features but is more stable. I use mainline for my needs, including in production.
The really interesting point is that nginx considers mainline to be more reliable than stable because stable does not receive all bug fixes, only the critical ones.
[1] explains which version should you use. (I probably go with mainline).
All the newest features are added to mainline releases. By the time most of the bugs are fixed, their version is renumbered and branch is forked to make a stable release.
[2] is where you see the information about upcoming nginx releases.