Puckering is fabric that has been pulled in by the stitching and has nowhere to go. It shows as ripples around the design, usually worse on the sides than the top and bottom, and it is nearly always the sum of several small mistakes rather than one big one.
Partly. Press from the back over a towel and let the piece cool flat; light puckering will relax. Fabric that has genuinely been pulled out of shape by an over-dense design will not fully recover, which is why a test sew on a scrap costs less than a ruined garment.
Work through it in order: loosen the density by 0.05 mm, add or increase underlay, move to a heavier cut-away stabiliser, and hoop the fabric and stabiliser together rather than floating the fabric. Density and stabiliser between them account for most puckering.
Partly. Pressing from the back over a towel and letting the piece cool flat helps light puckering. Fabric that has been pulled out of shape by an over-dense design will not fully recover, which is why a test sew is cheaper than a ruined garment.