Recently the private rocket-ship company SpaceX managed to a) launch a rocket, b) have it not blow up, c) return a portion of the rocket for reuse later, d) on a floating barge in the middle of the ocean. I'll assume we all understand the significance of a) and b), but what's the big deal about c) and d)?
First, the reusing bit. Imagine that every single time you drove your car to work, as soon you arrived at your destination and got out, you incinerated it. Totally destroyed. Completely unusable. Want to go back home? Buy a new car. Take the kids to soccer? Shell out for a one-time-use van. Our current (and, really, entire past) rocket program is exactly that. The big tall boosters that do all the rocketing just get chucked into the ocean or burned up in the atmosphere. Only the teensy-tiny tip of the rocket actually makes it into space and sometimes gets returned.
That's kind of wasteful, so SpaceX developed a booster that heaves a payload up into the sky, then lands safely back to Earth. Polish it up, fill it up with rocket gas, and it's good to go again.
That brings us to d). Why the barge bit? Well, when a rocket goes off, it doesn't just go "up", it also goes "sideways". For example, by the time a rocket launched in California reaches space, it's somewhere over the eastern coast. To reuse the rocket, one option is to have it slow down and fly back to the landing zone. That's doable, but expensive, since you needs tons more fuel. Hence, the ocean barge. The rocket takes off, lofts its cargo into orbit, and lazily glides down to Earth.
All this makes access to space cheaper. Like, way incredibly stupendously cheaper. And that's good.