'French polishing' (sometimes just 'polishing' in the UK) is a term
often loosely used to describe any finishing technique involving a lot
of rubbing.  Correctly, it means a method of producing a very thin but
extremely shiny shellac finish on wood, exploiting the phenomenon of
surface tension.

Liquids are broadly divided into two phase classes; aqueous (water,
shellac dissolved in alcohol, etc.), and lipid (oily).  When two
liquids, aqueous and lipid, come in contact, they do not mix.  But the
interface between them forms a surface with very high surface tension.
This surface tension stretches the interface very tight and flat, and
thus very shiny, on a microscopic level.

The polisher takes a pad, saturated with linseed oil (lipid), and
applies a small amount of shellac dissolved in 'spirit' (aqueous).
While rubbing this around a special way, the solvent gradually
evaporates, causing the shellac to go hard.  If one does the final
stroke just so, the stiffened shellac 'captures' the tensioned
interface, leaving behind a very shiny surface.

Anyone who has been in the military service will remember 'spit
shining'.  This the same thing, with the phases in reverse.  The
solution of wax in mineral spirit ('Kiwi' shoe polish) on the boot
is the lipid, and the water soaked cotton wad is the aqueous; but
it ends up the same way.

Richard Vance