Foam is laid over the cap or garment and stitched through. Where the needle closes around the edge of each shape it perforates the foam, and everything outside the design is torn off, leaving the stitched shapes standing proud.
That only works when the file was planned for foam. Too little coverage and the foam peeps through; loose edges and the waste clings on in ragged bits that have to be picked off before the cap can be sold.
Puff is a popular cap upgrade for club and teamwear caps and promotional merchandise. Many business logos carry a thin strapline or small print that will not hold foam, so we raise the bold parts and keep the rest flat.
Raising every element of a logo usually ruins the fine parts. We say which elements are too fine for foam and plan a design with the bold shapes raised and the detail stitched flat.