Astronomers use two basic methods to find planets around other stars: watching to see if a star dims when a planet passes in front of it, and watching to see if a star wobbles when a planet orbits around it. Neither of these methods are very good at seeing planets directly, but a giant zeppelin-mounted aerial starshade might be able to change that.
You know how if you're trying to see something up near the sun, you hold up your hand to shade your eyes? That's the idea behind a starshade: it sits somewhere in between a telescope and a star, and blocks out most of the light from the star to make it easier to see things close by it, like exoplanets.
The original concept for the starshade (which made it into NASA's 2011 strategic plan) was to send a huge starshade spacecraft out 80,000 miles in front of a space-based telescope (like the James Webb Space Telescope), where it would spend three years reducing light from target stars by a factor of about 10 billion to help spot planets around them. This technique is good for searching for solar systems within about 32 light years of Earth, which could represent a population of several thousand exoplanets.
A space-based starshade could happen by 2018 or so, but in the meantime, NASA is going to start a little bit smaller down here on Earth by using a zeppelin to hold a starshade above a telescope on the ground for a few days to see how well it works. NASA will be using Eureka, a 246-foot modern zepp with carbon fiber struts and a non-explodey helium-filled envelope that we've taken a ride in before. The idea behind this mission isn't so much to try and find anything, but rather to learn how the starshade is likely to work to practice for a potential three billion dollar deep-space version in the next five years or so.