Claudiu on SharePoint

Scenario: 
You open the web part it in edit mode, and under the Advanced section, the Target Audience box is missing.

How To:
browse to Central Administration -> System Settings -> Manage Services on server.
start User Profile Service

browse to  Open Central Administration -> Application Management -> Manage Service Applications.
create create a NEW User Profile Service Application (of make sure the existing one is started)

At this point the Target Audience box should be showing for your web part.