I cannot access the description of a group like this:
$web = Get-SPWeb "http.//yourUrl"
$web.SiteGroups | %{write-host $_.Name, $_.Description}
According to this, the description value is in fact stored as "About Me" in the DB-table AllUserData.
Using the group web service and $SPService.GetGroupCollectionFromWeb() also retreives groups without description.
How to read the description property of an SPGroup?