The majority of asteroids are scattered in a belt lying between the orbits of Mars and Jupiter. Some of the rocky travelers do come closer to home, making it all the way to the inner solar system. It's the bits of NEAs that break off the parent mass and reach Earth that become the familiar meteors of our night sky. For astronomers asteroids are a treasure-trove of information. In a very real sense they are a kind of construction debris left over from the time when the solar system was being assembled.
Asteroids are either proto-planets that never made it or planets that blew apart in collision.
If astronomers could learn more about the composition and structure of asteroids they'd have better shot at understanding how our, and perhaps other, planetary systems formed. There are other reasons asteroids are of interest. It's estimated that a half-mile asteroid holds about one trillion dollars' worth of iron, nickel, cobalt, and platinum. That could make somebody's day. On the flip side there is also the small point that any collision with a moderate sized asteroid could wipe out a good fraction of all life on Earth.