Short Answer: Databases typically make searching easier and more reliable
Longer Explanation: Databases are organized by subjects or topics, contain filters, and provide access to some sources difficult to obtain elsewhere.
Scholarly (Peer-Reviewed) Resources: Sometimes an instructor requires peer-reviewed or scholarly resources; databases are often the best method to obtain these resources.
Databases work similar to other search engines; however, Google throws you around to an array of sources -- some reliable, some not-so-reliable. A database keeps you centrally located, sort of how Amazon works. When I shop on Amazon, I can search for almost anything (usually books and cat toys), and I know that Amazon won't send me to Target or Walmart. There are pros and cons to this, but in most cases, a database has access to resources I can't obtain through a search engine.