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.
It's more even than most other developed countries, but it's easy to see there are _significantly_ fewer 0-4s than 30-34. In fact, there are less of every 5-year age group than the 30-34s.
So yeah, that graph shows the US is, on average, getting older. Immigration helps patch the numbers a bit, but the US immigration system attracts older candidates than most.
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.