How to enable it? Go to: Setup - Customize - Search - Search Settings, scroll down to Lookup Settings and check objects that you need to enable for Enhanced Lookups.
What is the 'extra' when enable this feature?
- Ability to sort search result by any column
- Ability to search not just Name, but also All Fields in that object
- Ability to modify columns shown in the search result, to modify available columns in lookup result, go to Search Results in the object Search Layouts menu.
This is the same auto-completion, only the parent object (not child object) need to enable for enhanced lookups.
Before enabling Enhanced Lookups
After enabling Enhanced Lookups
Reference: Enabling Enhanced Lookups