With a calculated property you can access the $_.Entity.Name value

Get-VMHost |
Get-AdvancedSetting -Name Syslog.global.logDirUnique |
Set-AdvancedSetting -Value $True -Confirm:$False |
Select @{N='VMHost';E={$_.Entity.Name}},Name,Value,Type,Description |
Format-Table -AutoSize

can we kind of break this down a bit, I'm kind of PowerShell dumb/noob.  

When the Get-VMHost command gets piped into the Get-AdvancedSettings command is that executed for each host like a for next loop, or are the values all cached in something like an array and executed all at once after all vmhosts are contacted?

A PowerShell, and PowerCLI, cmdlet returns objects that are placed one-by-one in the pipeline.
That pipeline passes these objects, again one-by-one, to the next cmdlet in the chain.

A calculated property on a Select-Object cmdlet allows you to specify an expression (in the E part).
That expression can refer to a nested property, or can even a complete code block.