I agree with Raggiemom, that's called raw edge applique. Best if you use a product like "steam-a-seam 2" and press it on first. If you are fortunate enough to have a special applique stitch on your machine use that. If not you also can use a blanket stitch or zig-zag stitch, but you will want to adjust your stitch so that it is just small enough to reach both background fabric and applique. Hope that helps.