AllowNull is used to permit explicit use of $null as a value for a Mandatory parameter:

function Test-AllowNull {
    [CmdletBinding()]
    param (
        [Parameter(Mandatory)]
        [AllowNull()]
        [Object]$Parameter1
    )
}

AllowNull is effective for array parameters, and for parameters that use Object as a type. AllowNull is not effective for string parameters as the null value is cast to an empty string, and an empty string is still not permitted.