Population pyramids represent graphically the age/gender structure of a population, i.e. how many men and women of a given age (or age group) are living in the population. They are a specific kind of histograms, in which (always): the male population is shown on the left side of the graph, and the female population on the right; the youngest are the "base" of the pyramid, whereas the oldest are at its top; the very oldest are generally omitted from the representation of the pyramid because it is impossible to depict this open-ended interval that contains a few of the oldest-old; percentages are calculated using both sexes combined (i.e., the total population) as the denominator.
A lot can be read from population pyramids: we can trace the history of a population, as well as project its future. In particular, one can infer the potential for population growth from a population pyramid. The two pyramids in the picture below represent typical populations.
The first pyramid, representing countries in West Africa, is typical of a population with high fertility and high mortality: high fertility means that there are a lot of children in the population and so the base of the pyramid is wide. By comparison, its top is very narrow because 1) mortality is high and people do not frequently reach the most advanced ages, but especially 2) due to high fertility, children systematically outnumber adults and the elderlies.
A few countries (mostly in Europe), on the other hand, have reached zero population growth or are experiencing negative growth because of low birth rates and an old age structure coupled with minimal net migration (countries in Europe try to close their borders to new immigration). In such countries, the base of the age pyramid becomes narrower than its upper parts, it is "shrinking".