astronomy - Why is a new moon not the same as a solar eclipse?

Forgive the elementary nature of this question:

Because a new moon occurs when the moon is positioned between the earth and sun, doesn't this also mean that somewhere on the Earth, a solar eclipse (or partial eclipse) is happening?

What, then, is the difference between a solar eclipse and a new moon?

Answer

Briefly: Because the moon's orbit "wobbles" up and down, so it isn't always in the plane of the earth's orbit around the sun.

There's a 2D plane you can form from the ellipse of the earth's orbit and the sun. This plane is known as the ecliptic. The moon's orbit is not exactly in the ecliptic at all times; see this (slightly overcomplicated) picture from Wikipedia:

So the moon has got its own orbital plane, separate from the ecliptic. This orbital plane "wobbles" around - there are two points of the lunar orbital plane which intercept the ecliptic, known as the "nodes," and these nodes rotate around the earth periodically. The moon will only pass right in front of the sun and cause an eclipse when one of the two nodes is along the line of sight to the sun and right in the ecliptic plane (hence the name "ecliptic").