According to thishttp://qnundrum.com/answer.php?q=981116
the failure of the 8.1 update may be due to a problem on Microsoft's side.
There doesn't seem to be anything the user can do except try again.
There may be a problem updating the tweaked version of Windows 8 that's running on your laptop (assuming you're using the Windows 8 that shipped with the laptop and not a retail version of Windows 8).
Having "updated" from Windows 8 to 8.1 on one of my computers, I wouldn't recommend the update.
Just keep your Windows security updates up to date.
Wait a couple of months and try again with 8.1 if you really want the update.
But it brought no improvements to my computer, and may have slowed it down.
It's not a necessary update, and unless you want to "prettify" the Start screen there's not much it will do for you.