Welcome to TenForums, @Griesel.

You are on version 1511, the Fall Update released in November 2015. You are probably being prompted with the Anniversary Update from August 2016, this will be listed in Update and Security as the 'Features Update to Windows 10, version 1607'. You system specs say you are using Pro, did you tick the 'defer updates' box? Is there a reason you want to stay on 1511?

Defer updates is a delay, not a total block. You are effectively switching your machine from the Current Branch to the Current Branch for Business.

Microsoft Technet said:

When Microsoft officially releases a feature update for Windows 10, that update is marked for CB, making it available to any PC not configured to defer feature updates so that those devices can immediately install it....

...Windows 10 clients in the CBB servicing branch receive the same build of Windows 10 as those in the CB servicing branch, just at a later time. CB releases are transitioned to CBB after about 4 months...

...Basically, CBB is a configuration state, meaning that if a computer has the Defer Updates and Upgrades flag enabled—either through Group Policy, a mobile device management product like Microsoft Intune, or manually on the client—it’s considered to be in the CBB servicing branch...

Overview of Windows as a service (Windows 10)

1607 was released to the CBB on 29th Nov 2016, so can no longer be deferred.
Windows 10 release information - current branch, build history

Bree is correct.
I have had 1511 with "Defer Upgrades" set for some time now and today I had a surprise 1607 downloaded, so it is going out to everyone that doesn't have it.

I did tick 'Defer updates'. Together with the Cumulative Update ver 1511 there is also a request to download 'Feature update to Windows 10, version 1607', which I have downloaded but the installation failed.
So, in short... 'Defer updates' ticked, and both Version 1511 and 1607 request to be downloaded again

Griesel said:

Together with the Cumulative Update ver 1511 there is also a request to download 'Feature update to Windows 10, version 1607', which I have downloaded but the installation failed.

Now that it's on the Current Branch for Business the 'Feature update to Windows 10, version 1607' can no longer be deferred. If you really must it can be hidden, though being now considered 'ready for business use' I can't think of a good reason to stay on 1511.
Windows Updates - Hide or Show in Windows 10

Did these updates fail when using Windows Update? If so, try a manual install. The latest CU for 1511 (KB3210721) can be downloaded from the Microsoft Update Catalog (KB3210721)

The media to upgrade to 1607 can be made using the Media Creation Tool.
Windows 10 ISO Download

I have done the manual install of the 1511 from the MS Update catalogue. I cannot understand therefore that Windows Update still ask for it to be downloaded.
Re the upgrade to 1607: I am a bit scared to do that when one reads the comments people had with the installation

Griesel said:

Re the upgrade to 1607: I am a bit scared to do that when one reads the comments people had with the installation

What about the hundreds of millions of people who have no problem with 1607 and, thus, don't comment on it?

Griesel said:

Re the upgrade to 1607: I am a bit scared to do that when one reads the comments people had with the installation

If you are nervous (as I was before taking the free upgrade to the RTM 10240 back in July 2015) then make a system image on an external HDD first. In fact, I restored my image to a spare HDD first (just to be sure) and still have it available to swap back in should I ever need Windows 7 again. Actually, just make a system image any way, you never know when your HDD may fail on you.

I used Backup & Restore to make my system image, but by all accounts here Macrium Reflect is a far better solution.