Life as we know it needs a place to live, grow, and evolve.  Planets are the
best such environments we know; so the search for extraterrestrial life must
begin with the search for planets.  We're pretty sure we've found all the large
planets in our own solar system; so the search for extrasolar planets, or
"exoplanets," is an important frontier of astronomical research today.

The problem is, planets are very small and very, very dim compared to stars.
Whereas we find stars readily just by looking outward from Earth, planets 
are nearly invisible with our current imaging technology.  But although taking
a picture of a planet is still beyond our grasp, we can use existing tools to
find some planets another way: by their motions around the stars they orbit.