What will be the role of gravitational waves in future physics? What does this discovery mean for us? Can it lead to a better understanding of the cosmos?
 A: I'd say the discovery of gravitational waves is important, but not as earth-shattering as you might think.  We have had indirect evidence of gravitational waves for some time now (the Nobel Prize in Physics in 1993 was for this), and so the direct observation of gravitational waves is an impressive technological feat and a nice feather in the cap for general relativity, but also something that we pretty much expected to happen.  This is somewhat analogous to the detection of the Higgs boson, which was quite important but also somewhat expected.  In that vein, it probably would have been more exciting to NOT find the Higgs boson, and I'd say a similar sentiment is true for gravitational waves.  Essentially this discovery tells us general relativity is functioning as expected.  No crazy new surprises there.
Moving forward, gravitational waves are probably most likely to find applications in astronomy and astrophysics as another method of probing the cosmos.  As technology gets better, we will eventually be able to build gravitational telescopes that will give quite a good look into certain processes (like black hole mergers, early evolution of the cosmos, etc.) that are difficult to probe with electromagnetic waves (i.e. with visible light telescopes, radio telescopes, etc.).
This is certainly not to underplay the significance of LIGO's result.  As with any theory, general relativity requires repeated experimental tests and proof in order to be considered an accurate model of the physical world.  Unfortunately, however, this discovery does not signify some completely new and unpredicted realm of physics.
A: 1) Prove Einstein right
2) Ability to see some black holes
3) Possibly more visibility into early phases of Big Bang.
I have withdrawn the comments on "my doubts about being able to detect them by LIGO" because there is latest news, they did. Well it happens when one answers more than what was asked for. Timing was fantastic..
