On the new Samsung Galaxy S6, the following function is automatically activated in the messages app: "Pop-Up Display"
This function shows you each new SMS that you receive on your Samsung Galaxy S6 in a separate pop-up window when an app is open. This function is designed to help you to read the first few lines of text. Would you like to disable this feature on your Samsung Galaxy S6 and receiving no pop-up alerts for new SMS anymore, then proceed as follows:
Open on your Samsung Galaxy S6 from the home screen the menu and then the settings. In the settings scroll all the way down to the section "Applications" and tap on "Messages". You will now find in the next submenu the menu item "Notifications". Select it and you will be forwarded deeper in a submenu. In this you can see the "pop-up display" feature.
Erase here the hook in the checkbox to turn off the pop-up notification when a new SMS message comes in.
Have you removed the hook and you receive a new message on your Samsung Galaxy S6 now, then it will not be displayed as a pop-up.