There is a lot of information and formulas included in astronomy, but how does it apply to the lives of people living on Earth? How does this information help us in today's world?
There are a few technological developments which have come about because of astronomy (or, in many cases, because of the space exploration program, which is separate from the work that most astronomers do) and then turned out to be useful in other areas. Astronomical research itself rarely has a direct impact on people's lives, but in the pursuit of their research, astronomers often have to invent new instruments and techniques that produce spinoff technologies with broader applications. Some examples of these technologies include low-noise radio receivers (used in cell phones and many other applications) and parallel computing. Also, GPS would be inaccurate without relativity.
Nonetheless, I would agree that astronomy does not have many practical benefits to people's lives. The reason we do astronomy, I think, is that people are interested in learning about it - humans want to know how the universe came into being, what our place in it is, and what other objects exist within it. Basically, we are curious, and astronomy enriches our lives that way. I would argue that astronomy is certainly not the only sphere of human activity that falls in this category - I mean, you might as well ask how art benefits people, or religion, or music...
Note added March 2004: As a reader of this page has pointed out, astronomy has historically had plenty of practical uses! In ancient times, knowledge of the constellations and the motion of the stars and Sun in the sky was invaluable for the development of navigation. In fact, it is still used today - a precise knowledge of the positions of stars helps satellites orient themselves in space. However, the vast majority of work that astronomers do today does not involve measuring the positions of stars. The work that most astronomers do is more properly referred to as astrophysics, the study of physical conditions in faraway locations in the universe. I would maintain that this research does not have much direct, practical benefit to people's lives.
Note added June 2015: There is more information on the practical benefits of space exploration on NASA's site that discusses Benefits to You.
Note added March 2016: Here are two related discussions from our Reddit AMA events:
- How do you respond to people who say we shouldn't worry about astronomy research? (from July 2013)
- What practical real world value is there in the study of astronomy? (from June 2014)
This answer was last updated on January 28, 2019.