Tempering untempered chocolate

Tempering chocolate is ensuring melted chocolate has a nice shine and there are a few methods to do that:

• add grains of unmelted chocolate and stir (which is the seeding method you're referring to)
• let it cool down while stirring
  (which is the most labour-intensive method, but the easiest to do if you've never done this before)
  which answers all of your questions as now you know what tempering is, how to get out of the chicken-and-egg situation, how to very first chocolate was ever tempered etc... :-)

As most chocolate recipes are made by professional Chocolatiers, they don't have time to perform the old tried-and-trusted granny method so they'll tend to use the seeding method...

This is what tempered chocolate should look like:

P.S. If this is the very first time you're making your own chocolates, drop this step entirely: it's just the look and feel that'll change as they will look very professional. (I never temper my chocolate as I only care about the taste and without tempering they'll look like they're "home-made") ;-)
P.P.S. There is never any chicken-and-egg situation: if you think any of those situations through till the end you'll realise the egg was first because dinosaurs laid eggs long before there were any chickens! :-)

I know there is already an accepted answer here, but I thought I would fill in some more precise details (although they might not be super-helpful for the casual, at-home chocolate maker). When chocolatiers need to temper chocolate and they don't have any already-tempered chocolate, the technique they use is a bit more specialized than to stir it while it cools. Specifically, they use a technique called "tabling," which is the most traditional method of tempering. Tabling is actually a pretty fast method, but requires some specialized equipment and skill, and it only works well for certain medium-sized batches of chocolate.

Tempering is all about temperature, agitation, and time. The general process is to: 1. melt all the crystals, 2. while agitating, cool the chocolate, 3. re-warm the chocolate to melt out unstable crystals, 4. keep the chocolate at the right temperature during use. It is the agitation at a particular temperature that creates the correct type of crystals to seed the chocolate.

With the seeding and incomplete melting methods, step two is basically accomplished by stirring in unmelted, tempered chocolate.

With tabling, you pour about half the melted chocolate onto a marble slab and then continually agitate it with a bench scrapper and palate knife (or similar tools). The marble will cool the chocolate down more quickly, and the agitation will cause crystals to form. When the tabled chocolate has thickened, it is returned to the bowl, where the warmer, untabled chocolate will melt out any of the incorrect crystals, and the remaining correct crystals serve as seed crystals to temper the entire batch of chocolate.

This is not always a very practical method for the casual chocolate maker, as it requires a very clean marble slab, some skill that you can only gain through practice, and the willingness to get chocolate all over everything in your kitchen.

While I don't agree that the only thing tempering gets you is a better look, I do agree that if you're a beginner and are making chocolates for yourself (or family and friends), it's okay to skip the tempering step. Your chocolates may look a little funky, or may not hold up well to being in very warm rooms, but tabling untempered chocolate is probably not worth it for small batches of home-made goodies.