I know a lot of people are confused by the terms grain and bias but it's really very simple. It just refers to the way the threads are woven in the fabric.
So when we talk about straight of grain, we're talking about threads that run parallel to the selvage here. And when you stretch, you won't see hardly any give. There won't be any give, really, very little.
When you talk about cross-grain, those are the threads running the other direction and you'll see, you'll get a little bit more stretch there. And so it's really important when you cut patches for quilts, that they're cut on the straight of grain or the cross-grain.
What you really want to avoid is bias and those are, and that's really the 45 degree angle of the thread. And you can see when I pull that, that really stretches a lot. And sometimes you do want to cut things on the bias. If you need a curve or you want to make binding for a scalloped hem, the bias is your friend. You really want to be able to do that. But most of the time you're going to want a nice straight piece that won't stretch. And for that you have to cut on the straight of grain.
I hope that clears up any confusion about straight grain and bias.