Why do I have two notifications when I get emails from gmail? I don't understand why I get two notifications on my phone every time I get an email. Is my phone running emails from two different apps? It's HTC One Mini, running Android 4.4.2.


Screenshot (click for larger variant)
You are running two email applications. 

From your screenshot the one with the big "N" is the Gmail appliction the other is from the HTC Email application, called email. 

You can remove your account from either, or disable the whole application if that suits better. 

To remove the account from HTC Email.


Press the "Application Menu" button at the bottom of your HTC device's screen.
Scroll to the "Email" icon, then tap it once to launch the program. If the application opens to the inbox of one of your accounts, press the "Back" button at the bottom of the phone to return to the "Accounts" menu.
Touch and hold your finger on the account that you want to delete until a pop-up window opens on the screen.
Touch the "Remove Account" option.
Tap the "OK" button to remove the account.


Alternatively (since this doesn't seem to work on this device in particular):


Go to Settings
Click Applications
Click Mail
Click Clear Data 


As another alternative if the mail application is 'mail' rather than 'email' there is a remove account option in the settings. 



To remove a Google account

Go to Settings &gt; Accounts and sync &gt; Your Google Account Name 

You can either untick Gmail in the synch settings, OR click the button Remove Account to completely remove your Google account (which you may not want to do for obvious reasons).