Apps still in Activity Monitor after being closed?
Closing the last window of an application doesn't necessarily close the application.

For example, opening two TextEdit windows and then closing them both (kbd>Cmd-W or click the red close button top-left of window) will not close TextEdit. This allows one to click File>New (or Cmd-N) to open and work on a new TextEdit document.

You may be familiar with how Microsoft Windows manages applications. It actually opens a new instance of Firefox, for example, for each window that you open. On the Mac, that's not necessarily the case.

People who learn to use Microsoft Windows before learning the Mac are often confused at first because the Mac uses a different conceptual model. This is how Macs have always been, more or less. 

Mac users get used to typing Cmd-Q if they want to completely quit an application. Often, this is not necessary. But if your machine doesn't have much RAM, you may notice memory hogs like browsers slowing things down.