Interfacings are using in making garments to give the fabric body, to strengthen weak fabrics and/or to give reinforcement to parts that need support such as buttonholes.
Interfacings are used under the main fabric, usually applied to a facing, but can be applied directly to the main fabric.
Interfacings can be made of any fabric, but usually (these days anyway) are made from a non-woven fabric. Bespoke tailoring will most likely use sew-in interfacing rather than fusibles.
Fusible interfacings have a heat sensitive resin on the wrong side so that you can apply the interfacing to the garment fabric using an iron.