Below are the steps to enable Audience Targetting in Sharepoint List 2010 -
- Click the list or library that contains the item you want to target.
- On the list toolbar, click Settings, and then click List Settings or
Document Library Settings.
- Under General Settings, click Audience targeting settings.
- Select the Enable audience targeting check box.
When you enable audience targeting on a list or library, you can target each item in the list or library to an audience.
NOTE: If the SharePoint list or library already is enabled for audience targeting, the Target Audiences column appears.
You should also check with the service which determines Target Audience should be enabled and running.
It's SharePoint User Profile Service that depends on "User Profile Synchronization Service". So first check the Services via Central Administration -> System Settings -> Manage Services on server.
Please refer below link to check with the configuration