The content of the process block runs once for each value received from the pipeline. The built-in $_ variable may be used to access objects in the pipeline within the process block:

function Show-Pipeline {
    begin {
        $position = $myinvocation.PipelinePosition
        Write-Host "Pipeline position ${position}: Start"
    }

    process {
        Write-Host "Pipeline position ${position}: $_"
        $_
    }
}

When an object is passed to the pipeline, the start message will be shown before the numeric value:

PS> $result = 1..2 | Show-Pipeline
Pipeline position 1: Start
Pipeline position 1: 1
Pipeline position 1: 2

Adding Show-Pipeline to the end of the pipeline will show that begin executes twice before process runs:

PS> $result = 1..2 | Show-Pipeline | Show-Pipeline
Pipeline position 1: Start
Pipeline position 2: Start
Pipeline position 1: 1
Pipeline position 2: 1
Pipeline position 1: 2
Pipeline position 2: 2

The $result variable will contain the output of the last Show-Pipeline command.