As described last September by Rhett Allen:
Then why doesn’t the bottom of the slinky fall as the top is let go? I think the best thing is to think of the slinky as a system. When it is let get, the center of mass certainly accelerates downward (like any falling object). However, at the same time, the slinky (spring) is compressing to its relaxed length. This means that top and bottom are accelerating towards the center of mass of the slinky at the same time the center of mass is accelerating downward.This is - arguably - a good analogue of thinking about individual components versus systems. If you look only at individual components of an overall system, you can very well come up with a series of rules that describe the conditions of the components that are being observed. It would even be possible to describe how these components seem to go against the rules that we know OUGHT to be governing other objects. However, assuming objects that are part of a system operate the same as when they are in a system is (arguably) a faulty way of thinking about the objects in question.
When looking only at the end of a slinky, it seems to levitate until the point that the mass of the rest of the slinky crashes down upon it. When looking at a tether ball swinging around its pole, it seems to exhibit centrifugal forces until the point that it stops moving. When looking at an astronaut in a capsule, s/he looks to be floating freely until s/he returns to Earth.
All of these things are examples of having the incorrect frame of reference; of merely looking at the components.
Still, enough of the discussion about depth of the topic; enjoy the slinky video and the explanation.