Having email access "on the go" can be very convenient, but you may reach the point with your Android device that you don't want to continue receiving messages on a certain account. While you can't log out of only Gmail, you can remove your entire Google account from your device, though this also removes data from other Google apps, like Calendar and Photos. Alternatively, you can stop receiving Gmail messages but continue keep using other Google apps by disabling Gmail sync, though technically you will still be logged in.
To remove your Gmail account, along with other apps associated with your Google account, you first need to open "Settings" by tapping the "All apps" option on the Home screen. Then, depending on your device, either tap "Google" in the "Accounts" section, or tap "Accounts" and then "Google." Finally, you should tap the account you want to remove and then the menu button in the top-right corner of the screen where you will see the "Remove account" option.
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To disable synchronization for Gmail only, you should tap the "All apps" option at the Home screen and then tap "Settings." Depending on your specific device, you should then tap "Google" under the "Accounts" heading, or else tap "Accounts" and then "Google." Your Gmail profile should be displayed there, and when you tap on it, you can tap on the "Gmail" option to remove the check next to it, which will disable future synchronization for that Gmail account.