What do these two computer messages mean?

After starting my laptop (Windows 10) came only.

"6 sec until the data check, skip with any key"

(I skipped because I did not care about it).

Later, a window opened:

"Restart your computer to fix drive errors"

(I could not use it because the window closed too fast)

What does all this mean?

Not much - and good. Can sometimes take 10 minutes

To do something?

Wait and watch

Disk check. This makes Windows itself if there's a fault or the PC is greasy.

Here is a video of how to start it manually.

The hard drive should be examined for possible errors. These will be corrected, if possible.

Such an investigation can happen occasionally. It is one of the maintenance tasks that Windows regularly performs.

You can also trigger it manually from the command line.

(=> chkdsk)

The message usually indicates that Windows thinks it has detected an error on the drive and therefore wants to run the Checkdisk program once to have a closer look.

You should also do this quietly (even if the PC start is delayed by that), depending on the result, Windows can fix the errors or give you more hints. Should there be any unrecoverable errors that may indicate a failure of the drive soon, you should then as soon as possible to secure your important data.