The word Finial comes from the Latin Finis - the end - so actually it is quite apt as the year is finishing - but I only realised that connection just now. I love finials, stone ones in particular. I look out for them and admire the mastery of carving. By old writers the architectural term is frequently applied to a pinnacle (more about pinnacles to follow), and usually confined to a bunch of foliage which terminates pinnacles, canopies and pediments in Gothic architecture. The introduction of finials was at a time when crockets (more about them to follow too), were popular, to which they bear a close affinity. The leaves used in finials often resemble those used on crockets, and sometimes four joined together would make up a finial. Spires are often topped with finials.
Beautiful examples exist at King's College, Cambridge which my latest lino-cut attempts to show. Where gables support ornamental decoration or finish in the form of a final, they are sometimes known as hip-knobs.
These are some more modern ones - Five Finials by Ian Hamilton Finlay (with Peter Coates)