What is the purpose of the small arrow pointing to applications in the Dock
On a Mac, these "arrows" are dock indicators for which apps are currently opened. (the arrows exist in up to 10.4 tiger, but since 10.5 leopard are now little lights)

The Mac OS revolves around an application based system, as opposed to Windows' window based approach. What i mean by this is, that in Windows (before 7), closing the last remaining window of an application (such as Firefox), quits the process. This means that the next time Firefox is used, it needs to be loaded again.

The Mac OS however, is application based. Applications are launched and remain open regardless if the windows have been closed. These running applications get a dock indicator, while they are open. This system, although consuming more system resources, means that (for example) Firefox is really snappy to open, since the application has been open all along, and doesn't need to be loaded again just because all the windows were previously closed.

Hope that helps, feel free to comment anything I can clarify on!