Welcome to Android Central! Are you using the Gmail app or the stock Email app? You're not really meant to sign out of your email accounts on your devices. Signing out of Gmail would mean signing out of your Google account, which would mean removing your Google account. Some 3rd party email apps might let you do this--I think the Yahoo Mail app has this option. Rather than signing out, you should make sure you have a good screenlock set up, to protect all of the data on your phone.
I'm curious--how do you sign out of your Gmail account on your Samsung phone?