It's actually the selvage edge. It is the woven edge that does not ravel (have loose threads that you can pull off). On fabric that is freshly cut from a bolt, it is the 2 edges opposite the folded edge. Often, it is a different color from the rest of the fabric, and may be printed with the fabric company name, and little round dots of the different colors used in printing the fabric.
Because this does not stretch or "give" like cut fabric, the selvage edges should be removed before cutting out quilt pieces. Usually 1/4" to 1/2" is enough.
I think you mean "selvage". That is the raw edge of the woven fabric. When you buy a length of fabric, selvage refers to the edge NOT cut. Some fabrics have a more finished selvage edge than others, for example velvet versus cotton knit.
The fabric between the seam and the cut edge is referred to as the seam allowance.
Fold the fabric on the diagonal so that one side edge is on the top edge. If you then cut along the shortest vertical edge, and unfold, you now have the largest square possible.
The way the fabric is woven gives it different properties in different directions. When you are cutting a pattern you want to get all the pieces on the same "grain", i.e. a piece that will be vertical on your body should not be cut diagonally on the peace of fabric (unless you cut all the pieces diagonally or on the bias). The grain of the fabric is the natural direction of the fabric. The selvage is the edge of the fabric. When you buy a piece of fabric from the roll, you get two cut edges that fray and two factory edges that look different from the rest of the fabric and don't fray. These edges are the selvage. If the grain of the fabric runs from selvage to selvage that means the natural direction of the fabric (that you should use to line up your pattern pieces) runs straight across the fabric from factory edge to factory edge.
The scissors you describe sound like buttonhole scissors. They are used to cut open a buttonhole after it has been sewn into fabric by a sewing machine and they don't cut through the edge of the fabric.
That is the bias. When you have a pattern that states "cut on bias" the pattern piece would be placed in a fastion that would be a "diagonal line against fabric grain". Pattern pieces cut in this fashion are sometimes more difficult to sew because when fabric is cut on the bias it gives the cut edge more of a stretch.
A grain of fabric refers to the direction of the threads in the fabric. Fabrics have three grains: lengthwise grain (parallel to the selvage edge), crosswise grain (perpendicular to the selvage edge), and bias grain (45-degree angle to the lengthwise or crosswise grain). Each grain behaves differently when fabric is cut or manipulated.
If your fabric is 45" wide then I would go for a yard (36"): cut three (3) 10" strips from selvage edge to selvage edge; then cut each strip into five (5) 8" lengths. This all depends upon if your fabric has a nap or pattern. If you need to reverse the lay out, then: cut four (4) 8" strips from selvage edge to selvage ddge; then cut each strip into rour (4) 10" lengths, leaving one extra.
The finished edge of fabric is called the selvage.
Fabric projects are hemmed to finish the edge. Without a hem, the edge of a woven fabric can fray or unravel. When the fabric is hemmed (either by folding under the fabric, or by using a serger), the edge of the fabric is reinforced and prevented from fraying.
Cut a piece of fabric so that it is 2 inches longer and 2 inches wider than the tablecloth you want to make.Then iron each side under 1/2 inch, and then repeat. This should be folded towards the wrong side of the fabric, adn cover the unfinished edge of the fabric.Then, sew along each folded edge of the fabric, 1/4 inch from the edge.
Serging or zigzag stitching a fabric keeps the fabric from unraveling.Serging trims the loose threads and encloses the edge in a thread casing.If a serger is not available, zigzag stitching the edge will enforce the fabric edge and keep it from unraveling.