Do any of your user-installed apps have the button not greyed-out?
This feature hasn't been standard since 4.0, but some manufacturers have added it back. The fact that you have the button at all suggests your phone supports it, but it also requires the app to allow it. Many app developers don't (and of course no pre-installed app can be moved), so if a particular app has it greyed-out it most likely just means that app doesn't support it. If none of them allow it then it may suggest a problem.