When you do continuous curves, you stitch an arc within the shape from corner to corner, then continue on to the next corner, arcing inside the block and to the next corner, all around. It's an updated version of stitching a quarter inch within the shape, but it doesn't require you to break the thread, so there aren't pesky tails to knot and bury. It's possible to quilt an entire large section of squares with continuous curves, by following a specific pathway, and completing the entire quilting without stopping or breaking the thread. If I knew how to post drawings on here, I'd be able to show you.
Maybe if you google "continuous curves", you can find a tutorial. If not, let me know and I'll describe the pathway.