Press the multitasking button and locate the app you want on screen. On the bottom right of it there should be a 'tack' icon in blue. Tap that and now the app is 'locked' on the screen. Screen touch is still registered, you just can't exit the app without 'unpinning' it first.
You must have this option enabled in your settings, though. Lock screen and security, Other security Settings, Pin Windows (in the Advanced section).