An asymmetric tartan means that the stripes do not repeat in mirror image fashion (e.g., A-B-C-D-A-B-C-D would be asymmetric, as opposed to A-B-C-D-C-B-A-B-C etc. etc., which would be symmetric, because it has "pivot points" or "mirror points"). The same order is repeated in both the warp and the weft in tartan. An asymmetric non-tartan might have A-B-C-D-A-B-C-D in the warp and A-B-C-E-A-B-C-E in the weft.

If you want a picture, let me know.

Cheers!

Barb