If you want to be realistic, it is clear that Mario, Luigi, Peach, and the few other humans we know of are not native to the Mushroom Kingdom.

Somehow they went from Earth to this realm, where a peaceful kingdom inhabited by the Toads are threatened by Bowser the tyrant.

The humans elevate themselves to that of heroes using the mystical properties of the local plantlife. They seize the Toad kingdom as their own due to them lacking central leadership and self proclaim they are benevolent heroes. Peach becomes the defacto ruler, and Mario/Luigi are her enforcers.

Your welcome

But we've never actually seen ruling, we've seen her throw parties, race go karts, fight things, go on vacation, get kidnapped multiple times, turned into an evil tyrant, play football, play tennis, play board games, dress up like a cat, wear nothing at all, get captured by aliens, but we've never seen her do anything at all resembling the actions of a soverign leader from her. Even Bowser commands Koppas and organizes them, builds castles etc. 

I think she's just a figurehead with very oddly specific magical powers. The ability to float (for limited time), pull turnips out of anything solid, and the magic she has for the sole purpose of countering the magic that Bowsers forces used to turn the toad people into blocks, weeds, and other inanimate objects.

My theory -

Mario and Luigi are from Earth and are marooned in the Mushroom Kingdom. All other humans in the Marioverse are either from Earth or descended from humans who originated from Earth. Princess Peach is native to the Mushroom Kingdom but her ancestors were from Earth.

Since the Mushroom Kingdom is on a different world and probably in a different dimension to Earth due to its weird physics, the Superman effect comes into play, explaining the Mario Brothers powers. Some of these powers are evidently inherited by native humans, too - explaining Peach's powers.

The Yoshi's Island line, where the Mario Brothers are twin babies - that's got to be a different reality. Assuming the rule that you can never meet yourself if you go back in time, I reckon that in the game Partners in Time, Mario and Luigi (older and younger brother, native to Earth) went back in time and to a parallel reality where they teamed up with a version of their infant selves who were twins, and native to the Mushroom World. This makes both timelines possible, and settles any arguments about where Mario and Luigi were born, and whether or not they are twins.

My understanding was that Mario and Luigi were working as plumbers working in Brooklyn combating the Shellkreepers or "Koopas" coming out of the pipes when the source of these Koopas, a magical pipe, lead them to the Mushroom Kingdom (much like how the pipe in 3DWorld leads them to the land of the Pixies). The Mushroom Kingdom has a hierarchy of inhabitants ranging from lowly Goombas to Mushroom Retainers to humans such as the various Kings and Princess Peach Toadstool. The lower the class, the more mushroom-like the creature. The Goombas were unhappy with their lot in life and sided with King Koopa when he invaded. The mushroom Kingdom contains various diverse lands, some of which have their own king. There are other lands around, such as the Dinosaur Land that is the home of Yoshis, or the setting of the Gameboy games where Princess Daisy runs the show.

Well there's also the little fact that coherent storylines and geopolitical backstories aren't Nintendo's strong suit.

Gosh, those Princess Toadstool pics.

While I find it fun to discuss Zelda or Pokemon canon, Mario's canon is in too much of a mess due to a variety of reasons to even attempt to discuss it outside a couple of very specific games and aspects.

Too little daisy.

Princess Peach--crazy emotional. Just play Super Princess Peach to know for sure.