The thread/grain running the length of the fabric, parallel to the selvedges.
This lengthwise grain is also known as the Straight Grain or the Warp.
Woven fabric is made up of criss-crossed threads. The threads running the length are the stronger thread, while the threads running along the cut-edge of the fabric have a little more give in them.
Showing the lengthwise, crosswise and bias grain on a piece of fabric.
Pattern pieces are marked with a grainline arrow (in this image in blue for emphasis). This arrow needs to be placed on the lengthwise grain of the fabric.