How to prevent the screen of an android device to turn off during the execution of an Activity?

Add android:keepScreenOn="true" to some widget in your layout XML resource for this activity. So long as that widget is visible on the screen, the screen will not turn off automatically.

EDIT:

A WakeLock, as suggested by other answers, technically will work. But then you have to manually release the WakeLock (if you mess that up, the screen will stay on a long time). And, since you could mess it up, you need the WAKE_LOCK permission. Using keepScreenOn avoids all of that.