Can you guys explain the relavence for us cretins?
I would ignore the answers given thus far, or at least take them with a grain of salt.
The correct answer is multi-pronged:
1.) Gravitational waves are a fundamental prediction of Einstein's theory of General Relativity. When you have objects spinning in particular ways (in technical terms, any system with a non-zero quadrupole moment), you will generate gravitational waves. This year's discoveries were the final crucial tests of General Relativity, and it was by a landslide the hardest test.
2.) Gravitational waves will provide a robust, totally new metric to look into the universe. It's a totally new way of observing the universe; there's tons of systems we could never hope to see, but if we get better and better at detecting gravitational waves, we'll have a whole new perspective into the universe by looking at what creates gravitational waves, rather than exclusively what creates light (which was previously our only window into the universe).
2'.) This will be necessary if we want to probe into what happened near the Big Bang. Once scientists get very good at detecting gravitational waves and improve the technology, there will plausibly be a time (maybe 30 years, maybe 50) where we can have a reasonably pristine vantage point into the Big Bang. No light or particles survive that period of time, but gravity waves would have survived (because they interact so weakly and infrequently). So if we want to know about what was going on within the first second of the Big Bang, so far as we know, this is the unique way we can explore that.
3.) Gravitational waves provide an interesting new probe into whether or not General Relativity is true. They will become more precise, and possible deviations of GR could be discovered, which would be interesting.
4.) On theoretical grounds, the existence of gravitational waves --combined with our knowledge of quantum physics-- pretty much tells us without a doubt that gravitons are the correct perspective, even if we can't see a single graviton quanta right now. An important feature of quantum mechanics is that all radiation (i.e. gravitational waves are a form of radiation) must be quantized. I won't go into much on that topic, but it's pretty much a universally accepted position right now in fundamental physics.
First, a shift in the gravitational force indicates a heavy presence that doesn't emit light and can't readily be detected.
Although a gravitational wave is essentially a shift of the gravitational force, it has nothing necessarily to do with black holes. The technical requirement is that the source of the wave needs to be spinning in specific ways. In this case, it means you need to have two spinning planets orbiting around each other, and if you want the signal to be strong, they should be orbiting very quickly.
The gravitational waves that we have detected, however, have been from black holes that are of order 10 times the mass of our sun falling into each other.
Second, anything that is new in the scientific community, like realizing the collision of 2 black holes, will set the scientific world a twitter. Third, the collision of black holes proves, again, that black holes do exist (as if further proof of black holes were needed) and here might be a good example to study the effects of black holes. Black holes are one of the squirreliest objects in the sky that might lead to further research in time travel, etc. Hey, black holes are squirrelly.
It's great indirect evidence of black holes, yes, which adds to other indirect evidence of black holes.
It's one step closer to discovering where gravity comes from...and perhaps what created the universe.
This is vague, but more or less right on the money.