Ellipses occur on anything that's cylindrical and are sometimes described as flattened circles. Getting ellipses accurate and consistent throughout an object is crucial to getting an object to appear cylindrical.
Imagine you're standing, holding a mup of coffee in your hand. When you're holding the mup at waist height and you look down at the mug, you see the top of the mug as a perfect circle. Now bring the mug up to eye level and see how that 'circle' changes shape, becoming flattened out as an ellipse, because you are no longer looking at it from directly above. Now take a look at the curve at the bottom of the mug and you'll see it matches that of the top. (This, of course, presumes that you've a plain coffee mug, not a fancy one.)
In slightly more technical terms, the higher your viewpoint with regard to the object, the closer to a true circle an ellipse will be. Conversely, the lower your viewpoint is, the flatter the ellipse will be. As your viewpoint moves from above a cylindrical object down until you're looking at it side on, so the ellipse flattens out, as shown in the diagram.
In order for a cylindrical object such as a mug, vase, or bottle to look real in a painting, it's crucial that the ellipses are accurate. It's a common beginner's error to have ellipses on an object that are inconsistent, for example the top of the coffee cup is shown as a circle and the base as an ellipse. Or to draw the same ellipse on all the cylindrical objects in a composition, without consideration for viewpoint and what the actual ellipse on each object is.