Interfacing or interlining are products which strengthen and provide structure to your fabric and ultimately your projects. If you want your bag, purse or pouch to be soft and squidgy then a fleece type interfacing would work best however if you want your bag project to stand up, to have structure, then foam will achieve this result.
I fuse woven interfacing to all of my fabric pieces, interior (lining) and exterior, it strengthens (thickens it slightly) and makes the fabric easier to sew together, it doesn't slip when sewing. It also helps to prevent wrinkles if you apply it to your fabric before you apply foam.
Foam interfacing is my go to interfacing for all my bags, and even though I use woven interfacing, fabric still wrinkles, particularly when you turn your project right side out when complete, but they easily iron out, use a pressing cloth, lots of steam and tools such as a ham to put inside your bag so you can press edges and curves.