Recipes are all the different combinations you can make using drinks, desserts and toppings. As you level up you can make new recipes by purchasing new Equipment and making new combinations.
New recipes have to be made once to be unlocked and sold in your café. You can figure them out thanks to Koffsky and other customers' hints or by spending diamonds.
Note that customers start asking for new recipes even if you have not unlocked them yet. They will leave the café if you do not serve them -unless they ask for something else as well- but come back a little while later.