Hermaphroditus was the son of Aphrodite and Hermes, the messenger of Zeus. His name was created by combining the names of his parents. Hermaphroditus was loved by a nymph named Salmacis. Salmacis loved him so much, she wished to be united with him in order to always be with him. The union took place, and hence a person with both male and female characteristics was formed. Hermaphroditus is where we get our modern word, hermaphrodite, for a person with both male and female sexual characteristics.
The best story I was able to find about Hermaphroditus was by Ovid in The Metamorhoses. To save you from having to go find a copy, the story is written below. I used the translation by Horace Gregory.
Salmacis and Hermaphroditus
The story ended, but the strange romance
Had captured every ear. "Impossible,"
Some said; others insisted that the gods
Made all things possible except false Bacchus.
The sisters then called out to Alcithoe
And held their tongues. She ran her shuttle through
The busy loom, then spoke; "I shall not bore you
With telling how young Daphnis of Mount Ida
Was turned to stone: this by a girl who, jealous
Of another, fancied her love betrayed-
Such is the sting that burns refected lovers.
That story's too well known. Nor shall I tell
How Sithon, turning backside nature's law
Changed from a man to a woman's at his will,
Nor how the stones of Celmis were once friends
Of infant Jove, nor how Curetes came
From rain, nor how young Crocus and his loved one
The Twining Smilax changed to little flowers-
I shall enchant your souls with something new.
"The waters of the fountain Salmacis
Have earned an evil name: the men who take them
Become effeminate or merely zero-
Certainly less than men, which is well known.
The reason why has been a guarded secret.
The infant son of Mercury and Venus
Was nursed by naiads in Mount Ida's caves;
His pretty face showed who his parents were,
Even his name combined their names in Greek.
When he had reachedh the age of three-times-five
He left the pastures of stepmother Ida
To visit hills adn streams of foreign lands;
Boyish delight made rough foot-travel easy
And pleasure came with each strange thing he saw;
He drifted toward the cities of Lycia
Where the Carians settled near their gates,
And there he found a tempting pool of water
So clear that one could read its sandy depth.
No swamps grew there, rank grasses, nor black weeds;
Only the purest water flowed, and round it
Neat turf and dainty ferns as though they were
Eternal greenery. A nymph lived there
Who never stirred abroad, nor followed deer,
Nor entered friendly races with the girls,
Nor took out hunting license with Diana.
Her sisters, it was said, made fun of her,
Or scolded, 'Salmacis, pick up your spear'
Or, 'Have you lost your pretty painted quiver?'
'Why not take turns at getting exercise;
A life of ease gives pleasure to the chase.'
But Salmacis refused; she took a bath,
Gazed at her lovely arms and legs in the water,
And found her private pool a likely mirror
To show her how to rearrange her hair
Even with a boxwood comb. Then, lightly dressed,
She sank upon the turf, or sometimes wandered
To pick a garland of sweet-smelling flowers
Which grew nearby-and that day saw the boy;
O how she yearned to take him in her arms!
"Yet she held off awhile in coming near him;
Stood still a moment till her blood ran cool,
Plucked at her dress and calmly fixed her eyes;
When she was certain that she looked her best,
She chose her words and spoke: 'O lovely boy
If you are not a god, then you should be one,
Cupid himself-and if your birth was human
How proud, how pleased your parents should have been.
What happy brothers, if you had them, doting
Sisters, and O, the nurse who held you close
To reach her breast. But gladder than all these,
Your lucky bride. If she exists, then let
Our love take shelter in the shade; if not,
Then let us find our wedding bed.' She paused;
The boy flushed red, half innocent of love
Yet red and white increased his fragile beauty:
As apples ripen in a sun-swept meadow,
Or ivory brushed with paint, or the grey moon,
When brass urns sounding beat for her release
At hour of her eclipse, red under white,
Such were the colours that played across his face.
As the girl asked him for a sister's kiss
And was about to stroke his snow-white neck,
He cried, 'Leave me or I must run away-
Get out of here.' Salmacis, shaken, said,
'This place is yours, but stay, O darling stranger!'
Then turned as if to leave him there alone,
Walked slowly cautiously beyond his view,
Looked back, dropped to her knees behind a hedge.
Meanwhile the boy as though he were unseen
Strolled the green turf and stepping near its water
Tested the rippling surface with his toes,
Then dipped his feet and, charmed by flowing coolness
Of the stream, stripped off his clothes; and when she saw
Him naked, the girl was dazzled; her eyes shone
With blazing blinding light that Phoebus' face
Poured in a looking-glass, nor could she wait
To hold him naked in her arms. Striking
His arms against his sides, he leaped and dived
Overhand stroke, into the pool; his glittering body
Flashed and turned within clear waters, as if
It were of ivory or of white lilies seen
Through walls of glass. 'I've won, for he is mine,'
She cried, clothes torn away and naked, as she
Leaped to follow him, her arms about him fast,
Where, though he tried to shake her off, she clung,
Fastening his lips to hers, stroking his breast,
Surrounding him with arms, legs, lips, and hands
As though she were a snake caught by an eagle,
Who leaping from his claws wound her tall body
Around his head, and lashed his wings with her
Long tail, as though she were quick ivy tossing
Her vines round the thick body of a tree,
Or as the cuttlefish at deep sea's bottom
Captures its enemy-so she held to him.
The heir of Atlas struggled as he could
Against the pleasure that the girl desired,
But as clung to him as though their flesh were one
'Dear, naughty boy,' she said, 'to torture me;
But you won't get away. O gods in heaven,
Give me this blessing; clip him within my arms
Like this forever.' At which the gods agreed:
They grew one body, one face, one pair of arms
And legs, as one might graft branches upon
A tree, so two became nor boy nor girl
Neither yet both within a single body.
"When tmed Hermaphroditus learned his fate,
Knew that his bath had sent him to his doom,
To weakened members and a girlish voice,
He raised his hands and prayed, 'O Father, Mother,
Hear your poor son who carried both your names:
Make all who swim these waters impotent,
Half men, half women.' Which his parents heard
And gave the fountained pool its weird magic."
The story ended, yet King Minyas' daughters
Kept to their work, and by their actions showed
How little they respected the great god Bacchus,
Even on his feast day. Then like a blast
The noise of cymbals, trumpets, flutes, rang in
Their ears, and with each breath the air grew thick
With the rich smell of saffron and sweet myrrh;
As if by miracle their thread turned green,
Green shoots among the ivy-growing looms,
Weaving between the clustered grape and vine
That covered purple cloth and deep brocade.
Then twilight came between the dark and the light;
Within the evening darkness sunset glimmered
As though red twilight filled the air: house, rafters
Seemed to shake, lamps flamed as if wild fires leaped
From room to room; then apparitions came
Of great beasts roaring through shadow and wall.
Through smoke and fire the sisters groped their way
To escape the flames and, as they floated, tripped,
And almost fell, a delicate membrane spread
Over their legs and feet and thin wings shrouded
Their waving arms. Nor did they know how changed
They were, for darkness covered all. Their wings
Were featherless, yet they sufficed to carry
Small shrunken bodies whose voices grew as frail
As shrill as they. They haunted house and attic,
But not the forest, and hid in eaves and swung
From highest beams, avoiding light of day;
Even their name is of the vesper hour.