how is this even possible?

If you're a space nut, you already know that Elon Musk (who seems to be in a one-man space race against China) is going to build a rocket whose first couple of stages fly back to their launch sites and land propulsively after they're done with the boost phase. This takes a lot less than half of their fuel since they're (a) not carrying upper stages any more, (b) mostly empty at that point, and (c) able to take advantage of aerobraking. But still... chemical rockets are a pretty marginal business. What's the secret?

I think I know, and it relates to another feature of the rocket. The Falcon 9 can make its intended orbit with an engine out -- perhaps even multiple engines out, depending on the failure timing. This is an important safety feature and one that's required to carry people, just as airliners all have enough engines to be able to complete a takeoff if one fails. But engine out capability means you have to carry some extra fuel, to make up for the less optimal flight profile. If boost goes nominally, the boosters can use this extra fuel for the return phase. If it doesn't, and if the payload is more valuable than the booster, then an engine out now costs you a rocket. Which is still better than the current regime in which most rockets are entirely expendable and the best case is that the booster has to be mostly remanufactured after a salt water splashdown.