Dan Lewis in Now I know:
What’s going on here? The Slinky comes with a small, barely visible jet pack which allows– no, wait. It’s just physics, even if counterintuitively so.
Let’s start with gravity. Drop something — a ball, your cell phone (which certainly happens all too often), a Slinky, or anything, and gravity will start to pull it down. That’s pretty straightforward. It’s why the top of the Slinky immediately falls once released, and it’s why we expect the rest of the Slinky to fall as well. But that’s not the only force acting on the Slinky. There’s also the tension in the spring.
From the perspective of the Slinky’s bottom, the tension is an upward force. Literally, the tension is pulling the bottom of the Slinky back up toward the top. When you are holding the top end of the Slinky, tension is what keeps it from unraveling entirely and falling to the ground as it stretches and dangles. When you drop it, the spring’s tension doesn’t just disappear, It’s still there and, in this case, pulling up at the same rate that gravity is pulling it downward. So the bottom stays in place as the Slinky compresses.
But in the end, gravity wins. When the top and bottom meet, the tension goes to zero, and the bottom of the Slinky joins the top in its descent back to the ground.
More here. And a bonus video: