I realized that there is a special circumstance when the three-tap to define feature is not working!
Try the following:
1) Make sure your Mac's hardware allows the Apple multi-touch gestures.
2) Turn your volume on and check if there are any background applications running that do something when you type (such as an app that produces a sound when you type on the keyboard). The apps may be running in the background without you knowing or seeing them, so try using Activity Monitor to detect them. If you can not find any app, restart your computer with the "Reopen windows when logging back in" deselected.
3) Now go to System Preferences and the Accessibility tab. Deselect "Enable access for assistive devices". Restart your Mac again with the "Reopen windows when logging back in" deselected.
4) When you will restart your Mac, do not open any application and make sure they are all closed! Go to Safari, iWork, or TextEdit and check if the three-tap to define feature works there.
Is the problem now fixed? If not, you might have to get a new copy of the latest version of OS X by completely deleting the computer and reinstalling the system 😟. Here's how to do it: http://support.apple.com/kb/PH11273
This will take time and you may want to check twice before you proceed.