So what is the get-serverhealth command good for?
For starters, let’s look at the command and its output:
get-serverhealth -identity ds-l1-e2k13-01 |ft server,currenthealthsetstate,name,healthsetname,alertvalue,healthgroupname -auto
This produces the following output – Server Health XLXS file.
What you will notice is that there are several Health Groups listed: Customer Touch Points, Service Components, Server Resources and Key Dependencies. Within each Health Group is a grouping of Health Sets.
Customer Touch Points

Service Components

Server Resources

Key Dependencies

Now what can we learn from these Health Sets?

From the above screenshot you can see that there are two issues with the server, having to do with AutoDiscover, and both are set to Unhealthy. Microsoft has a set of troubleshooting steps for errors that come up in these health checks:
AutodiscoverSelfTestMonitor is unhealthy
AutoDiscover is unhealthy
If we were to examine one of these, the AutoDiscoverCTPMonitor, we can see that the ‘AutoDiscover is unhealthy’ article directory references our exact issue:

If we were to run the “Invoke-MonitoringProbe Autodiscover\AutodiscoverCtpProbe -Server server1.contoso.com | Format-List” command, we would hope to generate the error that this probe has detected.

From the error it seems that there I have not configured my External EWS directory. This can be confirmed in PowerShell:

Indeed, the error seems to be generated because I had not configured an external URL for EWS. I then set my EWS virtual directory

After this change was made, I’ve generated a new error:

As this server was meant for testing, multiple URLs are not configured and thus would lead me down a rabbit hole so to speak to remove all the issues. So as you can see, these monitors are very useful for determining what is wrong with your server.
Related Resources
Health Sets
All Health Set Troubleshooters
Running Invoke-MonitoringProbe ActiveSync\ActiveSyncCtpProbe -Server Exch1 | Format-List command
gives me this output WARNING: Index was out of range. Must be non-negative and less than the size of the collection.
Parameter name: index
What version of Exchange are you running?