A little background information can be useful when working with cotton woven fabrics. Fabric is woven by setting the warp threads securely, then weaving the weft threads in and out of the warp. I remember the distinction of those two terms in this way: warp threads run parallel to the selvage edge and could (theoretically) go on to infinity, hence, warp speed like Star Wars. The weft, or back and forth from selvage to selvage, filler threads, I liken to left (weft) and right. Anyway, that's how I roll. So what does this gibberish have to do with quilting, you are wondering.
It's the nature and mechanics of the weave that affect the behavior of the fabric as you work with it. Because of the process of setting the warp threads of the weave first, it is a more stable, taut set of threads. The process of adding the cross threads (weft) results in the up and over and down and over crossing of the warp threads (weaving action) that by it's very nature adds some slack in the weft. What this means is that when you are cutting fabric, the cuts that parallel the selvage will be quite stable. The cuts that are perpendicular (right angle to) the selvage will be a bit stretchy, or have "give" in the weave. You can use these properties to your advantage when cutting and sewing. For example, by cutting long strips for, say, Log Cabins, you may want to make the length cuts parallel to the selvage, and sew with these cuts on top when sewing. If you sew with cross-cut (weft cuts) on top, you can experience distortion of the pieces as the pressure of the sewing foot, steam pressing, and other motions add to changing the original cuts of the fabric pieces. Pooh, pooh, you say? Factor in small distortions, then multiply by several pieces in a quilt before you discount the importance of considering how you will cut and sew fabric pieces.
This knowledge of cutting can be used to work to your advantage even when some cuts (often necessary to conserve fabric) are cut parallel to weft. When the option is available and some cuts are on the warp, some on the weft, simply place the stable weave on top to keep the stretchy cross cut under control while stitching.
Use this knowledge when pressing. Steam can distort your components, especially if you use a pushing motion with the iron. Lift and move your iron if you must press while sewing, or better yet, reserve steam for final pressing. Now that you realize the right-to-left motion is not a stable weave direction, move your iron in the direction that is, when such might be an issue.