How is powershell commonly used in SQL server?
So the main thing is that you can set these up to be dynamic. You wouldn't have to log into each instance to find out the settings. It does make it easier to perform a health check and just keep track of the lot. I used it for Parsing Excel documents to SQL server. This turned out to be very simple instead of converting it to csv documents and importing from there. 

But what I would do is check into this site, it has a pretty good repository. A bit old though...

Additionally, Microsoft is making a huge amount of enhancements to powershell into SQL server. It was ignored previously as it was already a scripting language. Most people now are going into proper desired state configuration where you can spin up a SQL server instance with memory and all the settings you would like inside the SQL server instead of it just setting up the windows box and you needing to log into the SQL instance to run scripts. Pretty good post about it here.