What does thie message about embedded ICC profile mean?

You can learn about ICC profiles in the Photoshop help files.  Basically, they relate real colors to the numbers in your document.

And the message means what it says: the profile in the document is invalid (corrupt or incorrectly written) and is being ignored.

What it doesn't say (but the manual does) is that then the working space profile for that color mode will be used instead, replacing the defective profile with a known good one.  If you need to replace the profile, you can always do that with the Assign Profile command.

icc-profiles allocate an absolute color-value to the RGB-, CMYK- or other color-values of pixels.

If an image is saved without embedding the profile Photoshop will assume the Working Space (Edit > Color Settings).

To make it a bit clearer (maybe) a certain comination of R, G and B may indicate that a pixel is more red, darker, … than another pixel of the same image with another comination of R, G and B, but without a defined color space (as defined by the icc-profile) it is not clear what red it is supposed to be exactly.