This is an interesting question; I recommend you to look at wikipedia for a good answer:

From there I found that the typical compound for fabric softeners is dipalmitoylethyl hydroxyethylmonium methosulfate. Fabric softeners tend to be based on quaternary ammonium salts with one or two long alkyl chains. Some fabric softeners have cationic compounds that can be derived from imidazolinium, substituted amine salts, or quarternary alkoxy ammonium salts. One of the most common compounds of the early formulations was dihydrogenated tallow dimethyl ammonium chloride (DHTDMAC).

The chemical compounds in fabric softeners give different results on the fabric. Fabric softeners work by coating the surface of the cloth fibers with a thin layer of chemicals; these chemicals have lubricant properties and are electrically conductive, thus making the fibers feel smoother and preventing buildup of static electricity. Other functions are improvements of iron glide during ironing, increased resistance to stains, and reduction of wrinkling.

Cationic softeners bind by electrostatic attraction to the negatively charged groups on the surface of the fibers and neutralizing their charge; the long aliphatic chains are then oriented towards the outside of the fiber, imparting lubricity. Vinegar works on some materials in a similar way, as the hydrogen ions bind to the anionic groups on the fibers.