When first learning to sew, we usually play around with fabric getting our feet wet laying out our pattern in the most logical way we can think possible, optimizing our fabric use and using our best judgement. This can work out just fine for many in early sewing projects, but as you get more invested in sewing your own clothing may feel like your clothes are looking a tad funny, or hanging crooked (this absolutely happened to me). In order to troubleshoot some of these concerns (and before we get into laying out your pattern correctly, learning how to orient your fabric "on grain", and "blocking" your fabric), we first need to start with understanding some fundamentals of fabric and how it relates to your clothing.
The selvage is a finish on the edge of the fabric that binds the edge of the textile and is often a different color than the textile.
The selvage runs parallel with the lengthwise grain (warp) of the textile and is very important to become accustomed to when starting your endeavors in clothing construction. The threads that run parallel with the selvage are the strongest and have the most resisting stretch. The lengthwise grain is most often placed vertically in clothing to prevent any or sagging in your garments as the garment ages.
On the contrary the crosswise grain (weft) are the fibers that run perpendicular to the selvage. These are the fibers that weave between the lengthwise grain. (think of fabric on a loom). First, fibers are arranged taught vertically up and down on a loom (lengthwise grain/warp), and them horizontal fibers weave in and out, in and out, of the vertical fibers. Since the crosswise grain is taking a less direct path between the lengthwise grain bending and curving, they will have some give to them. This makes the crosswise grain a little more forgiving and will often have a little bit of slight stretch. We must be careful not to orient our patterns on the wrong direction or else you will have a bit of stretch and sagging where it is not ideal. Luckily, having a bit of stretch in one direction (around our circumference) is pretty ideal when it comes to clothes, how cool is that?!
Another thing to note when it comes to fabric is the true bias. This is not technically a grain but more of an important characteristic of fabric when cut on the diagonal. Woven fabric cut on a diagonal will have more stretch along the cut edge compared to the crosswise/lengthwise grain. True bias is when it is cut exactly at a 45 degree angle to the selvage (or intersects the warp/weft at a 45 degree angle). When you cut out a pattern, note that any cut line cut at an angle will be inclined to stretch a little so be careful with your cut pieces.
Bias cut garments are often incorporated into designs. For instance a bias cut dress, the fabric wraps around your body in a different manner than a dress "cut on the straight grain". This is due to its additionally stretching properties and different drape fabric possesses when draped on the bias. this property can also be taken advantage of when making "bias strips/tape/binding" for finishing curves such as necklines and armholes.
Bias Cut Dress:
Bias strips cut out on "true bias" in preparation for finishing neckline of garment: