Hey! That's My Fish! has got to be about the silliest possible theme for what is, when you get down to it, an abstract strategy game with surprising depth. True, its rules are sufficiently simple as to be accessible to quite young players, but as with any abstract strategy game, the ability to plan and think several moves ahead is critical. In other words, this is not exactly a kid's game.
Before game start, the players lay out hexagonal tiles in a set pattern. Each tile is printed with between one and three fish. Each player places penguins of their colors on tiles, pretty much as they wish; it can be played by up to four, and the number of starting penguins depends on the number of players (e.g., in a four player game, each starts with two). On your turn, you may move one of your penguins any distance in one of the six directions permitted by the hex grid -- but not through an empty hex, or a hex containing another player's penguin. When you move, you remove the hex you formerly occupied, and score between one and three points, as indicated by the number of fish on the tile.
The main strategic element of gameplay is working to isolate other players' penguins, trapping them in small areas; when this happens, and an area is isolated that contains only one penguin, the owner scores all tiles in the isolated area, and the penguin is removed from play. Maximizing score by getting high-fish hexes is a secondary but important strategic consideration.
What is striking and admirable about the game is the strategic depth it provides for a remarkably sparse rules set. As Eric Goldberg says, it is far harder to design a good, simple game than a good, complicated one, and Hey! That's My Fish! succeeds at the task.