The phrase 'linear metre' is used, for example, when giving the price of materials cut from a long legth. The easiest way to explain it is by giving an example.
Suppose that a carpet firm sells its product at �5 per square metre. It could, of course, just put up a sign saying "�5 per square metre". But it sells it's carpet in widths of 2m, so it labels the rolls "�10 per linear metre" meaning that a charge of �10 will be made for every 1m cut off the roll.
If the firm also sells the carpet on rolls 3m wide, it will label those rolls as "�15 per linear metre".
So a 'linear metre' is measured in the same way as an 'ordinary metre' but the figure which results from it (i.e. the price) actually takes into account the derived area.
Chris