Musk tweeted that the rocket booster used "almost all of the emergency crush core" which, according to the article, "helps soften the landing".

Can someone explain what this means? What is an emergency crush core?

Ah, I believe I understand now. Here's an older tweet from Musk which mostly explains it: "Crush core is aluminum honeycomb for energy absorption in the telescoping actuator. Easy to replace (if Falcon makes it back to port)."

This was a hot enough landing that they used a 3-engine hover-slam to reduce fuel usage. Their last attempt at a 3-engine landing burn was also their last landing failure. When a landing goes slightly wrong, the crush core is the first thing to go... and this time it successfully did its job.