Rayman, Globox, and the teensies have been wandering through the forest when... you know, things happen. Don't sweat the details. What you need to know is: you have to save the teensies by crusading through various levels roughly themed around fairytales/folklore.
You navigate the different worlds/levels by wandering along galleries and hopping into paintings with various different themes attached to them. If you wander about the level navigation for a moment you're bound to find something to do, and linearity is hardly important here.
The game plays and flows beautifully, with some really imaginative level design. It does everything you expect from a sidescrolling platformer: you run, you jump, you glide, you punch. Except it does all this with really rich, varied and imaginative level design. Legends sits somewhere between 2D Mario and old school Sonic in terms of the feel of the thing, leaning more toward the latter. It's not as quick as Sonic, but if you're good enough it has something of that smooth flow.
There are various sorts of levels on offer. For example, once certain levels are completed, a secondary level re-using some of its features (you might call it a 'remix' at a push) opens up. These are speed runs, but accuracy is critical if you even want to make it through, let alone do so in reasonable time.
Using Murfy adds some fun moments, too. Players can get him to perform certain actions like tickling large enemies or eating out sections of cake-based levels, adding a rewarding extra dimension to certain levels.
Rayman Legends is, all in all, a really fun little game with some great design behind it.