The story is told via drawings in Daedalus' sketchbook, and every few pages you flip through has an interactive element with Icarus in some kind of predicament. There is no dialogue, spoken or written, so it is up to the player to interpret what is going through Daedalus' mind from one page to the next.
That's pretty much it. The game is extremely short, perhaps five minutes in length from start to finish, but that is not entirely to its detriment. Because the story is so abstract - it's Daedalus coping with grief through art after all - a lot of what is being told is so open to interpretation that on repeated playthroughs you notice little missed details and gain a different insight into Daedalus' mind. Still, it would've been nice if the game offered at least ten minutes of playtime just to give it a little more substance.
The interactive sections of the game rely on very simplistic controls, mostly swiping across the screen, and are designed to be intuitive to anyone who would pick up the game. However, the very first interactive section is completely unintuitive and will act as a roadblock for your progress as you spend a disproportionate amount of time trying to figure out the controls. Ironic, considering that the blurb on the App Store and the research report that the designers wrote (9.9MB ZIP/PDF) about their game both loudly tout the game's intuitiveness. The rest of the interactive sections are pretty simplistic, but to save those of you who buy the game a mountain of frustration, the first puzzle is solved by repeatedly swiping upwards or downwards as is appropriate.
Between the charming sketchbook art style and the abstract narrative, iCarus is an interesting interactive art project that could inspire storytelling techniques in larger, more professional titles. Honestly, the game could be shown in a modern art gallery if put on display properly. However, as a game it is most decidedly amateur, so don't go in expecting a groundbreaking gaming experience. If you're a designer yourself, though, give it a go and see if iCarus can be your muse.