Spark plugs have two jobs.
1) To produce a very high temperature spark to ignite the air/fuel mixture as quickly as possible.
2) To fine tune the temperature of the combustion chamber. Number 2 is the "heat range" of the plug, an explanation better than my own (and other good stuff) can be found on this site:
Most plugs do this just fine, with each manufacturer being a little different in their specifications (i.e. a heat range of "5" in an NGK is not the same as a "5" in a Bosch). There are equivalency tables, but don't expect them to be too accurate.
So I'll just concern myself with topic Number 1).
To create a spark, we must produce so much voltage across the air gap that the air becomes ionized (the molecules split apart and the electrons fly willy-nilly). This creates very intense heat, hopefully plenty to ignite the compressed air/fuel mixture, and the plug has done it's job (#1).
The shape of the plug electrode is important. The sharper the electrodes (both of them!) become, the easier it is to ionize the air between them. If I take two smooth brass balls of 3" diameter and put 10,000 Volts across them, I can get a spark to jump when I push them to within about 0.125" of each other. If I take two long, sharp needles pointed at each other, that same 10,000 Volts will still spark when they are 1.5" apart! (For the technically minded: this can easily be seen from Gauss' law if you compare E between the extremes of either two point charges or two equally spaced infinite parallel planes).
There is also another good reason for sharp points
"unshrouding" the spark.
Imagine that we put a big flat plate over the tip of the ground electrode, thus shrouding the spark from the combustion chamber. The spark would still happen, and the mixture would probably still ignite, but the burn would have to go out, around the plate, and back in to the center of the combustion chamber, resulting in piston rock and detonation. We'd much prefer that the burn happen in a very smooth, ideally hemispherical manner to produce a smooth pressure curve inside that chamber. By keeping the electrodes sharp, we unshroud the spark as much as possible, allowing the maximum contact between the spark and the air/fuel mixture, making it ignite more easily and the burn spread more smoothly.
So it would seem that the sharper the electrodes, the better.
This would be true except for two caveats having to do with heat.:
Caveat 1: Too sharp a tip will melt the electrode.
If the temperature of the (spark plug electrode) tip reaches the melting point of the metal that it's made of - you can kiss it goodbye.
Here are the melting points of some commonly used metals (Celsius):
Zinc == 420
Aluminum == 660
Copper == 1083
Steel == 1400-1500
Platinum == 1772
Iridium == 2410
This problem is mainly concerned with the volume of metal at the spark tip - if the temperature even instantaneously reaches the melting point, some of that metal will disappear. You can see that Platinum and Iridium coated plugs can withstand significantly higher temperatures, and thus can have sharper tips than their steel or copper counterparts. To add insult to injury, if some of the metal does disappear from a very sharp tip, then you've actually opened up the spark gap some. To prevent that from happening, we have to start with a wider tip, such that any small amount that is eroded will not change the size or geometry of the tip by too much.
Caveat 2: Too sharp an electrode tip will create a "hot spot" in the combustion chamber.
Even if you don't reach the melting point of the metal, you can still get it glowing hot. If that tip is still glowing red hot when the next compression stroke comes about (two full engine revolutions since the last spark) that residual heat can actually ignite the air/fuel mixture before the spark is supposed to occur. This is pre-ignition. It generally creates even more heat - leaving the spark plug even hotter than the last time thus repeating the cycle until you melt a piston. Ouch!
To avoid this, we want a wide area near the tip to conduct as much heat away from the tip as possible.
Here are some of the thermal conductivities of some commonly used metals (Watts / centimeter*Kelvin) :
Zinc == 1.16
Aluminum == 2.37
Copper == 4.01
Steel == 0.70 - 0.82
Platinum == 0.716
Iridium == 1.47
You can easily see why Copper is the metal of choice for the core of the spark plug. It's just about the best thermal conductor on earth. Occasionally, you still find plugs with an aluminum core - stay away!
So, what we want is the sharpest tip possible such that it does not melt the electrode nor does it stay so hot as to cause pre-ignition. Let's break it down:
They have a low melting temperature and the tips will vaporize away - they have a very wide tip so each little bit that disappears will not change the gap size greatly, but they still must be inspected often to make sure there is sufficient electrode material left. They are great for very hot running engines which must avoid pre-ignition at all costs, since the wide tip will not stay hot(high boost forced induction and nitrous engines come to mind).
Platinum plugs are usually constructed similar to copper plugs except that they have a thin coating of Platinum sputtered onto the electrode tips, about 0.010" thick (a human hair is about 0.005" thick). Because of the high melting point of Platinum, the tips can be made significantly sharper without fear of the gap changing shape. But the copper core is still sufficient to whisk the heat away fairly quickly. These are great all-around plugs, particularly for use on NA engines, and they should last a very long time. Very high heat engines should probably not use them because the sharper tips may not conduct enough heat away to prevent pre-ignition under adverse conditions.
This is the new guy on the block. They are much like platinum plugs just with iridium in place of the platinum. Because of the extremely high melting point of iridium, they can have very sharp tips without risk of melting and they should last a very long time. These would be best for high-rpm NA engines where the sharpest tip is needed for the best spark, but there is little danger of pre-ignition....
** Disregard any BS about the electrical difference of the metals - the micro-ohm difference in 0.010" thickness of Copper vs. Iridium means exactly squat when there is a huge air gap equivalent to tens of mega-ohms of resistance right there in series with it.