mesh of a tatami mat; stitch spacing on tatami
Refers to the visible weave pattern or the distance between stitches on the surface of a tatami mat. Often used in set phrases like 畳の目を数える (to count the tatami stitches) when describing idle or bored behavior.
I killed time by counting the stitches on the tatami mat.
Compound of 畳 (tatami) + の (possessive particle) + 目 (eye, mesh, grain). The exact historical derivation is straightforward; the phrase literally means 'the eyes/mesh of tatami'.