An ellipse can be defined as the shape created when a plane intersects a cone at an angle to the cone's axis. It is one of the four conic sections. (the others are an circle, parabola and hyperbola).
In the above figure, there is a plane* that cuts through a cone. When the plane is parallel to the cone's base, the intersection of the cone and plane is a circle. But if the plane is tilted, the intersection becomes an ellipse.
In the the figure above, as you drag the plane, you can create both a circle and an ellipse. The shape on the left shows the view that is perpendicular to the plane - as if you were looking straight down on the plane.
If you were to keep tilting the plane until it is parallel to the cone sides, the intersection would become a parabola. If you kept going until the plane was vertical, the intersection becomes a hyperbola.
* The plane is drawn with edges for clarity, but in reality a plane goes on for ever in all directions.