NASA wanted their space shuttle program to be completely reusable. Sadly, due to budget cuts, only the actual shuttle was reusable, and the boosters were ditched. On the other hand, Space X wanted to save as much money and as many resources as they could.
On the right is a picture of Space X's Falcon Heavy rocket, designed to, as the name suggests, lift a large payload into space, and on the plus side, at a much cheaper cost than before. On the left is a clip of the two "small" side boosters landing simultaneously after the Falcon Heavy's test flight yesterday. Sadly, the main booster missed the landing barge in the ocean and was lost.
By saving the boosters, we can save a lot of money and time that would be spent into making new ones for every launch.
Also, if you didn't know, the Falcon Heavy was carrying Elon Musk's personal car, a Tesla Roadster. They put a dummy in a space suit in the driver's seat, put "Don't Panic" on the display, and the radio, even though you can't hear it, is playing "Space Oddity." Or "Rocket Man." I don't remember.
If you want to check out more, here's the link to SpaceX's livestream, which also has the videos of the test flight, and a simulation of the test flight which are pretty cool.