What is the meaning of “Body Electric”?

I Sing the Body Electric is a famous poem by Walt Whitman, one of the twelve poems which comprised the first edition of Leaves of Grass (1856/67). In it, he celebrates the glories of existence, explores themes of the body, its parts and its whole, the interconnectedness of body and soul, the sensuality of the body, and equality and interconnectedness of us all (including between races.) The sensuality is prominently discussed to the degree that his publishers tried to have him remove it.

It may confuse some why someone would write about a body electric. We tend to think of electricity as a recent "tool".

Electricity was actually known in ancient times. Amber and similar substances, when rubbed (something like a balloon today) gave off an electrical charge. This was used in ancient medicine as early as 2600 BC (as were electric eels and magnets). The word first appeared in print (in English) in the 1640s, used by physician Sir Thomas Browne (1605-1682), apparently coined as Modern Latin electricus (literally resembling amber) by English physicist William Gilbert (1540-1603) in treatise De Magnete (1600), from Latin electrum (amber), from Greek elektron (amber).

The phrase Body Electric first appeared in 1746, in a reading of a paper on electricity in the body, given/written by a doctor, M. le Monnier the younger, who quotes an earlier treatise on the electrical nature of the body.

The following are some lines from Whitman's poem, which, taken out of context, do little to portray this work, but may help to answer the question.

I sing the body electric,
The armies of those I love engirth me and I engirth them,
They will not let me off till I go with them, respond to them,
And discorrupt them, and charge them full with the charge of the soul.

The love of the body of man or woman balks account, the body itself balks account, That of the male is perfect, and that of the female is perfect....
I have perceiv’d that to be with those I like is enough...
This is the female form... It attracts with fierce undeniable attraction...

A man’s body at auction...
Gentlemen look on this wonder...
A woman's body at auction... Do you not see that these are exactly the same to all in all nations and times all over the earth?

There are almost countless references to The Body Electric, from music to medicine to yoga.

The 2012 song, Body Electric, alludes to Whitman in the lyric: "Whitman is my daddy."
Ray Bradbury published I Sing the Body Electric, a science fiction anthology.
It is the name of the 100th Twilight Zone episode.
I Sing the Body Electric is the title and first line of a song Fame.
I Sing the Body Electric is the title of a 1972 Columbia Records album by the jazz fusion group Weather Report.
I Sing the Body Electric is the title of a 2011 song by the trip hop band Arms and Sleepers.

What does it mean? She is evoking Whitman's praise of the body and its sensuality, the oneness of all people.

At 18, she moved to the Bronx to attend Fordham University, studying a branch of philosophy known as metaphysics because "it bridged the gap between God and science. I was interested in God and how technology could bring us closer to finding out where we came from and why." She said, "that was when my musical experience began. I kind of found people for myself." She has had problems with substance abuse and found helping others with the same to be very meaningful.

Elvis is my daddy, Marilyn's my mother,
Jesus is my bestest friend.

Elvis and Marilyn were both very noted for their sensuality. Jesus preached loving each other, and she found (comfort/truth?) in Him.

Dancing and grinding in the pale moonlight. Grand Ole Opry, we're feeling alright...

Sensuality.

I sing the body electric,
I'm on fire, sing that body electric.

Whitman is my daddy, Monaco's my mother, Diamonds are my bestest friend.
Heaven is my baby, suicide's her father,
Opulence is the end.

Del Rey has long admired Monaco for being a symbol of a luxurious lifestyle. It represents luxury and richness (opulence). Another famous beauty, Hollywood's Grace Kelly, married the prince of Monaco, becoming a Princess (and such became a fantasy for American girls).

Or at least I pretend...
I pretend I'm not hurt and go about the world like I'm having fun

The fact that she pretends means she knows the body is at least partly (?more?) a superficial comfort. That heaven is her baby, yet suicide's her (the baby's) father tells us that the life she's led hasn't been easy, but the hard parts are a part of something beautiful anyway.