The groove they are talking about is something that happens when the book is finished, I think. Best to clear it with them.
However, this is purely from a design point of view, you should have text/important items 10mm away from the spine area.
Once the book is finished, it's creased, and the extra crease on the cover creates a hinge/groove, and it's undesirable to have text going through this groove.
This creates a hinge for the spine.
You wouldn't want text too close to the extra crease that creates the hinge, it would look awful.
Again - check with the printers if this is what they mean.
Thanks so much, you have given a clue in your words of what I need to do and what they had difficulty explaining in English. Sometimes it just gets lost in translation.. So thanks very much for your reply, it is much appreciated.
Just to note - the picture of the book, the groove refers to the line on the front cover (not the crease on the side).