Gmail app on your mobile works as a email client for non gmail accounts. But you wont get any of powerful features of gmail for your non gmail email addresses. Gmail has one of the best and powerful features like spam protection, inbox organization and even Google Now cards (for Android users). Until now these features are exclusive to @gmail email addresses only.
Starting today, you can Gmailify your inbox’s of Yahoo! Mail or Hotmail/Outlook.com. With this you will get all the goodness that comes from gmail to your non gmail email accounts.