Well, the moon’s orbit is not in the exact same plane as the Earth’s.
Picture this way: we draw a line between the Earth (simplifying by leaving out the fact that the Earth is a body of perceptible size, and that its rotating) and the Sun (simplifying by ditto). We draw the Moon’s orbit (yes, I know that the Moon cannot be said to orbit the Earth in the same way that the Earth orbits the Sun, or that Io orbits Jupiter. Go away). If the drawing is in a flat plane, the orbit always intersects that line.
But, this is all happening in a 3-dimensional space. That orbit, in 3-space, can actually intercept the line, or be above or below it. If the synodic period of the Moon (interval between moonrise and moonrise as seen from a constant point on the Earth) were an exact divisor of the orbital period, the Moon would always be in the same point in its orbit, it would always (or never) be in the same plane as the Sun-Earth line, and we would have a solar eclipse at every (or no) new moon.
Often, there are “partial” eclipses, where a portion of Sun’s disk, but not all of it, is obscured, for just this reason.
Since the Moon’s orbit is not circular, but elliptical, its apparent diameter varies somewhat. Ordinarily, we don’t even notice – but if an eclipse occurs when the Moon is near apogee, and its apparent size is distinctly smaller than the Sun’s, we get an “annular” eclipse, where a thin ring of light is visible around the obscured disk.
The orbital mechanics are such that a fair number of solar eclipses do occur – between two and five each yearr, IIRC. But a lot of them are partial (not impressive) or annular (not much more impressive). Or else, they occur out in the middle of the Pacific, where no one but a few albatrosses and maybe a passing ship can see them.
You-didn’t-ask-but-I’m-telling-you-anyway: the same thing applies to Neptune and Pluto. On a flat page, their orbits appear to intersect. Actually, Pluto’s orbit is inclined at (I think) 17° to the ecliptic (and thereby to Neptune’s orbit, to a good first approximation); the two don’t come anywhere near each other.
“Kings die, and leave their crowns to their sons. Shmuel HaKatan took all the treasures in the world, and went away.”