If you want to get Audience membership for a particular user then you can use GetUserAudienceIDs method. In this method you can pass the UserName of the user.
I have wrote a sample PowerShell script to achieve this.
$site = Get–SPSite “http://SharePoint-2013”
$web = $site.Openweb()
$context = [Microsoft.Office.Server.ServerContext]::GetContext($site)
$audMgr= new–object Microsoft.Office.Server.Audience.AudienceManager($context)
[System.Collections.ArrayList]$audIDNames = audMgr.GetUserAudienceIDs(“Contoso\\Garthf”, $true, $web);
$audNameID = new–object Microsoft.Office.Server.Audience.AudienceNameID()
for ($i=0;$i –lt $audIDNames.Count; $i++)
{ Write–Host $audIDNames[$i].AudienceName }