When the Sun is eclipsed by the Moon this Sunday, for many observers across much of the world it will be temporarily replaced by a beautiful ring of fire - a brilliant annulus of stellar plasma just peeking out around the dark lunar disk. This doesn't always happen, partial solar eclipses merely trim away a chunk of the solar disk, and true total eclipses perfectly blank out the visible surface of the Sun. It's all a matter of alignment between Sun-Moon-Earth and our mutual orbital gymnastics.
It is an interesting coincidence that the Moon should so nearly perfectly blot out the Sun, since there is really no physical reason why this has be the case. The Moon happens to be about 400 times smaller than the Sun, but the Sun happens to be about 400 times further from the Earth than the Moon is. So simple geometry tells us that the apparent disk of the Moon is almost exactly the size of the apparent disk of the Sun. Of course this match is not always quite the same, the Earth orbits the Sun in a modestly non-circular, elliptical, path and so our nearest and furthest distances (perihelion and aphelion) differ by about 3.3%. And the Moon's orbit has a roughly 10% difference between its near and far point to us, so the precise degree of total solar eclipse will vary a little as the apparent sizes of Sun and Moon vary. This Sunday the distance variations conspire to make the Moon appear 94.4% the size of the Sun.
However, on longer timescales the Earth-Moon system is not static. Tidally driven evolution of the orbits and spins of these two bodies results in a number of things. First, as we know well, the Moon's spin rate is matched to its orbital period so that it always has the same face to the Earth (except for some small librational wobbles). Second, because the Earth's spin is faster than the Moon's orbit, the tidal bulge raised on the Earth pulls on the lagging moon, gradually raising its orbit and slowing our day. Every year the Moon's orbit grows by some 3.8 centimeters and our day lengthens by about 0.000015 seconds.
At this present rate, in about 50 million years the Moon will never completely eclipse the Sun, it will simply appear too small on the sky. This orbital evolution also implies that total solar eclipses in the distant past would have been just that - completely obliterating the Sun from view. It is very likely that a scientifically minded Tyrannosaurus Rex never got to see the circle of fire, or Bailey's Beads in an eclipse.
So is there some great significance to the fact that we humans just happen to exist at a time when the Moon and Sun appear almost identically large in our skies? Nope, we're just landing in a window of opportunity that's probably about 100 million years wide, nothing obviously special, just rather good luck.