After pianist Carli Muñoz tells us about his formative musical years, he wraps up with:

Y ya, el resto es historia.

And that's it, the rest is history.

Caption 75, Carli Muñoz - Niñez

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Well, it's pretty easy for native English speakers: "El resto" means "the rest" or "the remainder."

Carli could just as well have used lo demás and the meaning would have been the same.

...lo demás es historia...
...the rest is history...

Lo demás also means "the rest" or "the remainder" and is reserved for referring to abstract concepts (such as "the story") or an indefinite/unspecific group of things.

Te amo y lo demás no importa. [abstract concept]
I love you and the rest is not important (nothing else matters).

Trae la valija negra y lo demás dejalo en el living. [things/stuff]
Bring the black suitcase and leave the rest (of it) in the living room.

When referring to people, the singular lo demás is not ever used, however the plural los demás is used (and used often):

Me siento tan feliz de ver la vida como los demás

I feel so happy to see life like all the rest (the way everyone else does)

Caption 23, Joselo - Sobriedad

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Muchos espectadores se fueron, pero los demás aplaudieron.
Many of the spectators left, but the rest applauded.

Los demas also comes into play if we are talking about specific remaining items in a group of things.

Yo quiero tres galletas. Puedes dar los demás a tus amigos.
I want three cookies. You can give the rest to your friends.

El resto can also be used when talking about people, or rather when talking about people as a singular group:

Muchos espectadores se fueron, pero el resto (de los espectadores) aplaudió.
Many of the spectators left, but the rest applauded.

Note that what we wouldn't want to do in the above example is use los restos (in an attempt to pluralize el resto), because we would no longer be talking about the remaining spectators, but rather about their "mortal remains."

Ubican, el pancito, los oritos, los alimentos en sí, en el lugar mismo donde que está ubicado en este caso, los restos mortales de sus familiares.

They place, the bread, the gold, the food itself, in the same place where it's located in this case, the mortal remains of their relatives.

Captions 12-14, Tradiciones indígenas - Visitando los difuntos

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Olga pidió que llevaran los restos de su padre a Roma, donde él vivió sus últimos años.
Olga asked that her father's remains be returned to Rome, where he spent his last years.

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If you'd like to bend your cabeza around this topic some more, there is a discussion in wordreference.com that you are sure to enjoy reading.