What does the "Force stop" button mean? When I go to Settings &gt; Applications &gt; Manage Applications &gt; Downloaded I see an application list. If I select some applications I see button "Force stop" active, but some applications have this button dimmed.

What does it mean? What happens if I press this button?

This button can't mean application running, since the applications with this button are not listed in Running section.

Can I list just applications which have the Force stop button active and uninstall them?



Android version: 3.2
As said in my comment to paco's answer, the information he gave is mostly correct: Most apps don't exit completely if you leave them, and no app should exit if you leave it via the "Home" button. Moreover, some apps have background services running which the user otherwise cannot quit.

Now there are some situations where you need an app (including its background services) to be stopped -- e.g. if you want to uninstall that app (or, in case of a system app, its updates). You will notice this when the "Force Stop" button is active, the "Uninstall" (or "Remove") button is grayed out -- but the latter gets activated when you stopped the app via "Force Stop". (If both buttons are grayed out, you can tell it's a system app, by the way -- which you cannot uninstall).

Btw: If the "Force Stop" button is grayed out ("dimmed" as you put it) it means that app is not currently running, nor has it any service running (at that moment).