I suppose that there are three descriptions of rod action: fast, medium and slow, and, of course, all points in between. Forget all the adjectives such as progressive, parabolic etc.
A fast action rod flexes predominantly at the tip
A medium rod has the action moving down the middle part of the rod
A slow action rod bends down into the grip.
Imagine gripping a common playing card on one edge and flicking it with the other hand, then listen for the sound. Next grip the card in the middle and flick, and finally grip it three quarters of the way down and flick again. The sound the card makes gets higher in pitch the more the card is forced to bend nearer the end.
This is exactly the same with a fly rod. If the tip only bends, the rod recovers very quickly, short tip movement equals fast action and tight loops. As the action moves down the rod the tip moves further and further taking longer and longer to recover, making larger loops and slowing down the rod.
Do not be misled by all the hype that tight loops are essential to ‘good’ rod action. A wide loop will allow a fly to be presented more slowly and delicately in situations that need it. When roll casting a slow action rod will roll the line out far more effectively than a fast action rod. For example, this can be seen when using greenheart rods both for roll and traditional spey casting. If one has a slower action rod the wider loop can be offset by using silk lines which are thinner and cut through the wind better. A similar effect can be seen with faster action rods.