Finish installing device software in Windows 8.1 Action Center

i assume you did a fresh install        windows 8.1 (or other)
then most devices have generic drivers -  or none
after starting the first time, windows will start instalklling correct drivers - so that's what happens to you
no malware

It's not malware, it's most likely some optional software downloaded from Microsoft Update such as the Microsoft Keyboard and Mouse Center or a device driver.

As I never use Microsoft's drivers for hardware (they've done more harm than good) and download my drivers from the manufacturers of the system, I simply turn these notifications off.

This is a PC that was preinstalled and also has a hidden restore partition.  All the drivers etc. were installed already (I should hope anyway).  As an extra note, the PC was logged on as a non-admin before being connected through a router to the Internet.  Admin credentials were entered only after the Norton Internet Security 2014 install asked for credentials.  It still bothers me that Windows will say that alegedly a driver needs to be installed, but won't tell you what it is or at least give a file or list of files to be installed.  Wouldn't there be some place in the registry that might show what supposedly is waiting to be installed?

>>  This is a PC that was preinstalled   <<   if all drivers were installed (are you sure?) then it's unlikely windows will reclaim one; was this a preinstall done by yourself - or how was it done?

It's a Best Buy preimaged machine.  It wasn't open box.  Brand new from the factory.  I hadn't tried explicitly forcing Windows update to run, and it didn't seem to indicate that it was ready to install updates yet that I noticed.

normally everything should be installed then - except updates; windows and others.
it's unlikely to be malware

I hadn't tried explicitly forcing Windows update to run, and it didn't seem to indicate that it was ready to install updates yet that I noticed.

You don't need to, Windows Update will try and install all updates automatically by default at (3AM every day I believe).

What's most likely happened is that Windows Update has installed what it needs to but requires your input to complete a some software it has downloaded. I know for me it was the Microsoft Keyboard and Mouse Center when I clicked on the Finish installing device software link. I just cancelled out of it when the setup prompt appeared and the message went away. If this is a brand new machine then you can safely click on it and see what it wants you to install.

I do understand your query though, I'm finding it hard myself to try and find out exactly what Windows wants to install when this prompt appears (short of actually clicking on it)!

Funny thing is, it only takes a minute or 2 to come up after connecting to the router (and thus to the internet).  I experimented by restoring this to factory default multiple times.  It has appeared to stay there through reboots.  I even left the preinstalled McAffee in place when I downloaded NIS downloader and ran the NIS downloader to grab the install files before disconnecting from the internet to uninstall McAffee and install NIS (all while logged in as non-admin).  At a certain point, I just decided to leave it and continue with other items, but the actual Windows updates did not try to install until I shut down the PC (74 updates).  I will check to see if the action center notice is still there (haven't looked at it since yesterday afternoon).

OK, I click on the Install button in action center, and I get the following:  
Do you want to allow the following program to make changes to this computer?
Program Name:  Device driver software installation
Verified publisher:  Microsoft Windows
File origin:  Hard drive on this computer
Program Location:  "C:\Windows\system32\newdev.exe" 6

I'm still confused as to what supposed driver it thinks it wants to install.  The last time that I reverted to the factory image, I did not install any hardware (admittedly I am using the keyboard and mouse from my old PC but they are nothing special).  But if it were the keyboard and mouse, why does the action center prompt always wait until I start going online after reimaging to put up a notice?

I'm still not really satified that Windows makes no attempt to identify what it wants to install.

that happens with a lot of windows problems - nothing new
i sure wish they would identify each time; it would make things a lot easier

The solution doesn't really give an answer to find out what Windows 8.1 is trying to install, but suggests either just letting it go through and hope you can identify if it is benevolent, if you can even find out what it is, or nuking from orbit.