The best rods demonstrate a progressive action under progressively increasing loads. Here are the words of wisdom of veteran rod designer Don Green:

In the ideal rod, the tip section of the rod flexes and loads to handle shorter casts. The rod should only flex into the midsection for making longer casts. The rod should only flex into the butt section when fighting a fish. The worst thing in the world is to "run out of butt". If the rod is flexing deep into the handle/grip while fighting a fish, you've got the wrong rod for the application.

That's a pretty broad statement he makes, and obviously the application for which you are buying the rod makes a big difference.

A light sensitive tip is oh-so-important for detecting that subtle bite while drift fishing, or allowing a fish to really chew on a trolled/mooched herring or a backtrolled/plunked Kwikfish, flexing the rod well into the mid-section without the fish feeling a lot of resistance until he has turned away with your goods. At that point, the reserve power in the butt section will bury the hook point home. A rod with this type of action is also popular with boondoggers/side-drifters. This is what most people refer to as a SLOw action.

Contrast that with jigging or backbouncing heavy leads, which requires you to lift a considerable weight repeatedly. A light tip in the first 10-12 inches is important for detecting the bite, but a good rod for these applications shouldn't flex much beyond that when lifting the lead. Otherwise you spend all day fighting the flex in the rod (before the lead even moves) just to properly work your goods. If the rod flexes into the midsection or deeper for anything less than a fish on, then you've got the wrong rod for the application. This is what is commonly referred to as FAST action.

Power can really be summed up by how much weight the rod can physically lift when it is bent into the butt section. The maximum line rating is a pretty good indicator of power.

Hope that helps.