Imagine you get into a car start the engine, touch the acceleration and go from 0 to 60 in the blink of an eye. You then take the wheel to turn right and instead of a smooth turn the car takes an immediate 90 degree turn.
This is how interface design feels without smooth transitions. It works, but it does not feel natural to the user. Animations can give your design the illusion of depth and lifelike motion, creating a more 3D space and giving the user the feeling of being inside the design.