This image shows a progression from a circle, with eccentricity $e = 0$, to a hyperbola, with eccentricity $e > 1$.
A circle can be considered as having two coincident foci; an ellipse has two distinct foci; a parabola has a single focus; a hyperbola has two distinct foci again.
As eccentricity increases from $0$ to $e < 1$, foci seem to move away from each other. But what does it happen in the limit case, when $e$ equals $1$? Where does the "second" focus move?
Unlike the other conic sections, the parabola has a single focus. It is obvious when observing the intersection of a cone with a plane in space. But when dealing with eccentricity, considering the parabola as a limit case of the ellipse, it is not so obvious.
Consider this definition of eccentricity:
$$e = \frac{c}{a}$$
where $c$ is the distance between the center of an ellipse and either of its two foci; $a$ is semimajor axis. The limit case $e = 1$ implies $a = c$: foci should somewhat be placed on the border of the ellipse. But this is not helpful.