It's called a population pyramid because the shape of that graph for a growing population is a pyramid. If you look at some of the African countries on that site (like, say, Uganda and the United Republic of Tanzania, if you're starting from the United States page), you can see they're closer to a pyramid shape because they have higher birth rates and higher mortality over time.

Also, on the graph you linked to, you can click on the line in the graph of population versus year to the right, and if you start back in the 1950s and work your way along to the present, you can see the big lump of the baby boomers getting older. That's why people say the United States has an aging population.