There is no physical reason why the moon fits precisely within the diameter of the sun.
It just so happens that on our little planet with sentient life, in which human life is present for only an incredibly small window, the time in which we are present and looking to the skies is when the diameter and distances of the sun and moon align so perfectly as to fit one within the other.
It turns out our moon has many seemingly strange properties. It's big but not very dense. Still a bit of a mystery how it formed, too. There are leading theories (ex. Mars-sized planet ramming into a young Earth) but not considered settled science just yet IIRC.
The number of systems which reach our intellectual capacity must all have certain aspects which make them completely unique, a rare feat in such a large and repetitive universe.
Sun's size is so big comparable to both earth and moon. When shadow of moon is spread on earth, shadow's radius is much smaller than moon's radius, unlike our conventional knowledge that shadows appear larger with distance. For people on earth who are in the path of totality, it appears as if moon has completly covered the sun.
This ought to fit nicely into some version of the anthropic principle. That either pensive critters like us specifically or life in more general terms for a variety of subtle reasons depend on just such a match of ratios.