In honor of the upcoming bicentennial of the birth of Charles Darwin, the January issue of Scientific American has evolution as its theme. One of my favorites is Testing Natural Selection, by H. Allen Orr, which has a nice explanation of how evolution works:
... the idea of natural selection is simplicity itself. Some kinds of organisms survive better in certain conditions than others do; such organisms leave more progeny and so become more common with time. The environment thus “selects” those organisms best adapted to present conditions. If environmental conditions change, organisms that happen to possess the most adaptive characteristics for those new conditions will come to predominate. Darwinism was revolutionary not because it made arcane claims about biology but because it suggested that nature’s underlying logic might be surprisingly simple.
There's also a useful diagram at the top of pages 46-47.
I'm going to take my own stab at explaining the basics of evolution with an overly-simplified analogy, inspired in part by the diagram in the Orr piece.
Differences in birth- and death rates change the proportions
Imagine you have a giant, slowly-spinning barrel labeled "Life." The barrel contains two types of 'organism': Cubes and balls. Each cube and each ball contains a miniature factory for making more of its kind. (That's 'reproduction.')
The Life barrel contains a bunch of square- and circular holes of different sizes. As the barrel spins, some of the cubes fall through some of the square holes and out of the Life barrel; some of the balls fall through some of the circular holes. (These holes represent death, a crucial player in evolution.)
Think about how differences in 'birth rate' and 'death rate' will change the proportions of cubes and balls over time:
Suppose that, on average, the cubes balls are able to 'give birth' to a few more of their own kind per day than are the balls cubes. Other things being equal, the barrel will contain increasingly-more balls than it does cubes as time goes on, because of this difference in 'birth rates.'
But suppose that balls also 'die' faster, because there are many more circular holes in the Life barrel than square holes; thus, far more balls fall out of the barrel than do cubes. Suppose that this higher 'death rate' for the balls more than offsets their higher 'birth rate.' Other things being equal, over time the cubes, not the balls, will come to dominate the barrel's population.
On balance, when a given cube eventually does die -- and they all do -- the odds are that it will leave more of its progeny in the barrel than will a given cube. Overall, the cubes are better adapted to life in the barrel than the balls.
Circumstances can change the birth- and death rates
But life in the barrel can change. Suppose that a freak lightning bolt burns another square hole into the barrel, and that mud clogs up some of the round holes. This increases the 'death rate' of the cubes and decreases that of the balls.
Now, the cubes no longer have quite the same evolutionary advantage over balls as they did before. Over time, we can expect to see the proportion of balls increase relative to the cubes.
The relative proportions of balls and cubes can change in other ways, too. For example, a cube could 'mistakenly' manufacture a 'child' cube that's too big to fit through the smaller square-shaped holes. (That's mutation.) The oversized child cube is likely to survive in the barrel longer than other cubes, meaning that it's likely to leave more progeny behind than they do.
And if the oversized cube's progeny are also oversized, what will we expect to see eventually? Over time, the relative proportion of normal-sized cubes will drop, because they 'die' at a faster rate than do the oversized ones.
* * *
That, in a nutshell, is evolution.