What is a linear meter? I'm just trying to understand the concept of a linear meter. 

I'm aware that rolls of fabrics can have different widths and depending on the width and need a shorter or longer part of this fabric. 

Am I understanding this correctly that linear meter is just an indication that the width might not be 1 meter and someone who orders this has to take the width of the particular fabric into account when ordering fabric?
This isn't just for fabric, but carpet and all sorts of material on rolls. A linear metre simply means 1 metre length off the roll. It says nothing at all about the width, which is usually more than a metre for fabric, but for some things may be much less.

The width should be specified elsewhere in the description, to allow you to calculate how much to buy. You are likely to need to take more into account than the total area, for all but the simplest project with plain fabric.