High-level: a standby is a second server, running the same version of PostgreSQL, the reads the real-time backup/WAL data from the primary server and restores it to its own files; so that at any given moment it is in sync with the primary and could take over for the primary should it encounter machine failure (or otherwise go offline).
My question was more of how to actualy do the update to a specific versions.
What are the commands to do it? normaly the default upgrade is for the latest version.
I'm not sure what is the recommndation. Should I just update directly to 9.3.16? It's very confusing how to do it somoothly.
Personally, I use Ubuntu and running <apt-get upgrade postgresql-9.5> works just fine for me...
The reason the docs don't cover this is because the docs assume installation from source. You need to inquire with whomever provided your packages as to how they work.
Typically one would just upgrade to the new patch release in a major version. While certainly possible I don't know of any situations where not doing that would be beneficial.
As for the release notes - they cannot cover every possible combination of upgrade paths. You'd need to read them and figure out how to adapt to your situation. They assume that once you are on a major release you are keeping up with the bugfix releases.
If you encounter a failure while/after running a minor update you either need to restore the executables from backup or see if your packaging system can help. I guess the answer would really depend on how things failed - and given that such failures are relatively rare little effort has gone on to make reversion within minor releases easier.
There is something to be said for standing up a new VM running the new binaries and falling back to the old VM running the old binaries if there is a problem. The data files want to be kept separate and mounted to the running VM with the desired version.