The rotary cutter is a blessing for anybody wanting to make straight edges, a huge improvement over tracing around a template with a pencil and then cutting along the line with a scissors. Rotary cutters, paired with rulers, make perfectly straight edges with very little work.
Although traditional quiltmakers have always worked with ruler-straight edges and seams in most block construction and when sewing blocks together, contemporary artists often prefer the looser look of freehand cutting. You still use the rotary cutter and mat, but instead of lining your blade up against a ruler you cut without a guide. Even when an edge/seam looks almost straight, you can see the artist's hand in a freehand line where you don't get that vibe from a ruler-cut line.
On the left, freehand straight lines; on the right, ruler-cut:
The problem with freehand cutting is friction. In an ideal world, your fabric wouldn't be the least bit slippery and your rotary cutter would be so sharp and roll so smoothly that it would cut a clean edge without pulling at all on the fabric. You would finish your cut with the two pieces of fabric exactly in their original places, so perfectly aligned that you would barely be able to see that they were cut at all. In the real world, the blade catches just a bit and pushes or drags the fabric along with it a hair as it rolls along; you'll often see a bubble of fabric moving ahead of the blade as it cuts. This is especially true if you are cutting two layers of fabric at the same time.
To prevent this, and to make sure that the cut goes exactly where you want it to, it's helpful to hold the fabric in place as you cut. For short cuts, you just hold it down with your fingers (being careful, of course, not to cut yourself). For longer cuts, anything over a foot, I like to hold the fabric in place with the plastic ruler, but keep the cutting line at least a quarter-inch away from the edge of the ruler. That way you get the best of both worlds: the freedom of the freehand cut, where you can wobble or curve your line if you want, plus the ease of cutting fabric that stays where it's supposed to.
Stay tuned for tips on how to sew not-straight pieces of fabric together and still have them come out perfectly flat.