In the Contacts web app, the Search functionality has been improved to enable you to find relevant results faster.
When you type in only one or two letters, the search returns only Contacts or Companies with last or first names starting with these letters. As you type more letters, the search extends to a full text search on all fields (email, phone, address,..).
Note that this functionality can be used to list contacts alphabetically by typing in the first letter of the name, and is designed to replace the alphabetical links previously used in Contact lists.
The results of the search by name are first returned in a Top Results section, followed by the results of the extended search in a More Results. The result screen displays first companies then contacts, but you can filter to only Companies or Contacts by clicking on the Tabs.