As others have indicated, it the Fn key is a special case handled internally. I'll provide the technical explanation.
When you press a key on a keyboard, the keyboard controller (a small IC chip inside the keyboard) detects the electrical circuit and processes it to decode which key was pressed and then sends the scancode to the motherboard. The operating system receives scancode from the BIOS and then performs whatever action it needs to in order to process that keypress.
With most keys, this is simple enough. If you press the A key, its keyboard controller sends the scancode to the motherboard which then passes it to the OS which in turn usually prints 'A'. (If the OS detects that one of the modifier keys is currently held down, then it may do something different. In fact, you can configure it to do whatever you want when the A key is pressed with or without modifiers.)
Now the Fn key is special. When you press it by itself, nothing happens because it is exclusively a modifier key and is not (generally) meant to do anything on its own. When you hold it and press another key, the keyboard controller detects that and looks in its built-in table to see if it is a known combination. If the combo is not in the table, then it just ignores it, but if the combo is in the table, then it looks up the associated scancode and sends that.
What does the OS end up seeing? It does not see the scancode for the Fn key and the scancode for the other key. Instead, it sees a single scancode associated with whatever function the Fn-combo has been set to. For example, if the laptop manufacturer has set the Fn+Down Arrow combo to reduce the volume, then the OS sees the scancode associated with the Volume Down, which some keyboards actually have.
So how does this explain why holding Fn on the laptop and pressing a key on an external keyboard does not work? Simple, because the keyboard in the laptop and the external one each have their own controllers. As far as the controller in the laptop sees, you pressed and released the Fn key and as far as the controller in the external one sees, you pressed and released the other key. What does the OS see? It sees that you only pressed the other key without any modifiers.
You can see that Fn key handling is special with a simple test. Plug two external keyboards into a laptop (thus giving you three keyboards). Hold the Ctrl key on one keyboard, the Shift key on another one, and then press the Escape key on the third. The Windows Task Manager should pop up. Why? Because Windows received the scancodes for all three keys, one from each of the three keyboards' controllers. (This was a Windows example, but pressing key combos in this manner should work the same in other operating systems. For example, even in DOS, you can reboot the system by pressing Ctrl+Alt+Delete on different keyboards.)
Note: the information about how the Fn is specially processed and the resulting limitations on its use are only general, based on common implementations. There is nothing stopping a laptop manufacturer from deciding to implement it differently and allow the user to remap the key to some other function, provide an emulated Fn key on external keyboards via some specific chord, etc. In fact, there is not even an official standard for the Fn key; most manufacturers just use the same implementation that others have used because it's cheaper and changing what users are accustomed to is usually not good.