The phrase "to separate the leaves" means to move or pull apart the individual parts of something, such as taking each leaf of a book or a plant and putting them apart from each other. Full definition
While potatoes are roasting, prepare the chard by separating the leaves from the stems. (coffeeandquinoa.com)
Remove the core from the lettuce and gently separate the leaves. (theharvestkitchen.com)
No matter how hard you try, you can not separate the left half of your field of view from the right or switch to seeing things in black and white. (scientificamerican.com)