Quilt binding is usually cut on the straight grain -- crosswise or lengthwise of the fabric, or binding is cut on the bias (diagonal) grain. There are advantages and disadvantages of each that I will explain in the paragraphs below.
Some quilters like to make straight grain or cross grain binding because they think it is easier to make and apply than bias binding. There is also a belief that straight or cross grain binding uses less fabric. Straight or cross grain binding strips are cut across the width of the fabric selvage to selvage or along the length of the fabric parallel to the selvage. Binding strips cut either in a crosswise or a lengthwise direction would be considered to be on the grain.
Some quilters prefer bias binding even if it has been thought of as more difficult to make and apply. It is also thought to take more fabric. Bias binding is not difficult to make nor does it take more fabric. Bias binding strips are cut on the bias or diagonal grain of the fabric. The easiest way to find the diagonal of the fabric is to use the 45 degree angle on your acrylic ruler or to fold an exact square of fabric in half on the diagonal and press. The line you press is the bias grain.
Straight Grain or Cross Grain Binding
The most common binding is cross grain binding. Strips are cut across the width of the fabric and then are pieced on the diagonal. The seams are pressed open. Straight grain binding is cut on the lengthwise grain and strips are also pieced on the diagonal. The slight advantage of cutting binding on the cross grain is the binding has a slight "give" or stretch if there is a necessity to ease when applying it to the edge of your quilt.
For cross grain binding if you cut 2 1/2" strips you will have 40 usable inches of fabric. When you piece the strips on the diagonal, you will loose almost three inches of each strip due to the seam and trimming off the waste triangle and selvage. You would need to cut enough strips to accommodate the seaming and waste. Cross grain binding works very well for square or rectangular quilts.
Straight grain binding is also cut in strips but the length will vary depending on the length of usable yardage. Again you will loose some length in the seaming the same as for the cross grain strips. Straight grain binding would be best used if some of the edges of your quilt top are bias. The straight grain would stabilize the stretchy bias edges of your quilt and help keep the quilt square. This binding might be best for a wall quilt or art quilt.
Either straight grain or cross grain binding does not have enough stretch or give to bind round edges, a curved edge, or scalloped edges of your quilt.
If you have a round edge, curved edge, or scalloped edged quilt you will need to use bias binding. The bias binding has "give" or stretches on the bias and it is able to curve around a circular portion on the outside of your quilt.
Many special treatment bindings are also cut on the bias. If you have a striped fabric, or any one way design, cutting binding on the bias adds a diagonal interest to the binding edge of your quilt.
Advantages of bias binding
Bias binding will wear longer than straight binding so in a bed quilt that is getting lots of use bias might be the better choice. The straight binding will have only one or two threads actually on the edge of the quilt. These few threads in the fabric right on the edge of the quilt will wear faster. Bias binding has stretch and flow and moves at the edge and won't wear as quickly.
Fabric amount comparison for bias and grain binding
Many quilters think that bias binding takes more fabric than straight binding. This is really not true -- if you calculate the square inches of fabric it takes to make straight or bias binding you will find the amount of fabric needed is about the same.
The main reason it appears to take more fabric for bias binding is that straight binding is usually cut from straight strips the width or length of the fabric and bias binding is usually cut from a large square. It only appears to take more yardage when cutting bias from a square but it really does not take any additional fabric. If you mathematically calculate the square inches of fabric needed for either type of binding it is approximately the same amount of fabric.
Flat Binding and French Fold Binding
French fold binding differs from flat binding. Flat binding is just that -- flat. It is usually cut 1 1/4" wide and is not folded before applying to the quilt. Flat binding is stitched right side of binding to right side of quilt top using a quarter inch seam. Then the binding is turned to the back and the quarter inch raw edge is folded under as it is hand stitched. If you are short on fabric flat binding might be an option as it doesn't need to be cut as wide not taking as much fabric. Only one layer of fabric is on the outer edge of your quilt.
French fold binding is cut wider -- usually 2 1/4" to 2 1/2" is standard. Then fold the pieced strips in half lengthwise with wrong sides together and press. It is then stitched to the quilt -- matching raw edges of binding with the raw edge of the quilt. Use a quarter inch seam. After stitching, turn binding to the back of the quilt and hand stitch. The folded edge is already finished and ready to stitch to the back of the quilt with no additional turning.
Using French fold binding -- either straight or bias -- will assure that even if the edge of the binding is wearing the inner layers of the quilt won't show because there is a second layer of binding behind the top layer. You won't have to replace French fold binding as often as single layer binding and the edge of the batting won't show because of the two layers.
Remember -- if you are making a planned quilt and know what fabric you will be using for binding, why not cut the square for bias binding or strips for straight binding at the same time you are cutting your strips and patches for piecing. Then label it by pinning the name of the quilt on a small scrap of paper to the binding fabric or strips. Then when the quilt is finished you will have your binding ready and won't have to hunt in your stash -- or worse have used all the fabric in another project.