A fabric softener sheet put in the dryer works much the way a liquid fabric softener does.
But it includes agents that disperse very small amounts of softening and antistatic components throughout the warm air that permeates the damp fabrics.
Fabric softening agents are surfactants, chemicals that reduce the tension at the surface where two different materials meet.
Soap and detergents are surfactants that reduce oil-water surface tensions and thus help wash out oily dirt.
Surfactant molecules have two components, one soluble in oil that resists water and one soluble in water.
Those used to soften fabrics have a high proportion of fatty material, generally long fatty chains, with water-soluble groups that may be anionic (negatively charged), cationic (positively charged) or nonionic (uncharged).
The fatty agent puts an extremely thin coating of oil at the interface of two moving surfaces, so they slip by each other easily and without friction.
Cationic or nonionic solubilizing groups help reduce static buildup resulting from the presence of negatively charged ions.
Dimethyl tallow ammonium chloride is a typical cationic softener and polyethylene glycol monostearate is a typical nonionic softener.