The backstory of Storked has it that the stork inadvertently dropped scads of penguin eggs all over Antarctica, and using your crack crew of penguin specialist, you must rescue them. What it basically means is that this is a puzzle game, and in each level, your penguins must find an egg, and get it to the baby basket somewhere else in the level.
As typical in puzzle games, there are a limited number of obstacles and elements you must use to solve the level, with additional elements added over time so that you're gradually introduced to the complexity of the system. In Storked's case, you have four penguins, not all of whom appear in each level, each of whom can move and kick the egg (no hands so they can't carry it), but each of whom has some special ability. Murray throws snowballs, the main use of which is to toggle levers that open doors or cause other changes on the level; Milton can use "gadgets" (gained by visiting "gadget booths" and pressing the up arrow), including a rocket pack, drill, diving mask, and teleporter; Tony is a brick who can hurl the egg over obstacles and lift crates; and Lily jumps. If multiple penguins exist on a level, you can change from one to the other at any time with one of the numeric keys.
Backspace undoes the last action, and "r" restarts the level, so you never get into a position you can't recover from; and the levels are designed with care and cleverness. There are four difficulty levels too, so there's both a degree of replayability, and a difficulty that even relatively small kids can play. There's also a level editor, and a fair number of fan-created levels on the developer's site (in addition to the 100 that come with the full game).
Hugely innovative? No, but cute, well conceived, with pretty good music and sound effects (I particularly like the "crunch" the penguins make when they eat fish), and who really needs more?
The demo contains only a handful of levels, but enough that you should get a sense of whether or not the game is worth plunking down actual samoleons for.