How does -InputObject parameter of the Sort-Object cmdlet work?

InputObject is a generic name used for a parameter that takes pipeline input. It's part of internal PowerShell naming convention and there is nothing special about it.

Your example doesn't work as you think it should, because when you pass a collection to the InputObject parameter it's treated as a single item and not unwrapped to individial elements, so it doesn't get sorted. This allows you to sort a collection of collections.

Consider this examples:

This is how Sort-Object works:

function Add-Quotes
{
    Param
    (
        [Parameter(ValueFromPipeline = $true)]
        $InputObject
    )

    Process
    {
        "'$InputObject'"
    }
}

Note that array is automatically unwrapped by the pipeline, then idividial items are assigned the $InputObject variable in each iteration and then processed in Process block:

PS> $items | Add-Quotes
'a'
'b'
'c'
'd'

But when you pass a collection to the InputObject it's not iterated over, because there is no pipeline to unwrap it:

PS> Add-Quotes -InputObject $items
'a b c d'

Sometimes it's a desired behavior, sometimes you need to unwrap collections no matter where they came from. In this case you use internal foreach loop to do so:

function Add-Quotes
{
    Param
    (
        [Parameter(ValueFromPipeline = $true)]
        [string[]]$InputObject
    )

    Process
    {
        foreach($item in $InputObject)
        {
            "'$item'"
        }
    }
}

PS > $items | Add-Quotes
'a'
'b'
'c'
'd'

PS > Add-Quotes -InputObject $items
'a'
'b'
'c'
'd'

Hope this makes it clear for you.