Pseudo-Apollodorus Library 1.47 [6.3]

When the gods had overcome the giants, Earth, still more enraged, had intercourse with Tartarus and brought forth Typhon in Cilicia, a hybrid between man and beast. In size and strength he surpassed all the offspring of Earth. As far as the thighs he was of human shape and of such prodigious bulk that he out-topped all the mountains, and his head often brushed the stars. One of his hands reached out to the west and the other to the east, and from them projected a hundred dragons' heads. From the thighs downward he had huge coils of vipers, which when drawn out, reached to his very head and emitted a loud hissing. His body was all winged: unkempt hair streamed on the wind from his head and cheeks; and fire flashed from his eyes.

Such and so great was Typhon when, hurling kindled rocks, he made for the very heaven with hissings and shouts, spouting a great jet of fire from his mouth. But when the gods saw him rushing at heaven, they made for Egypt in flight, and being pursued they changed their forms into those of animals. However, Zeus pelted Typhon at a distance with thunderbolts, and at close quarters struck him down with an adamantine sickle, and as he fled pursued him closely as far as Mount Casius, which overhangs Syria. There, seeing the monster sore wounded, he grappled with him. But Typhon twined about him and gripped him in his coils, and wresting the sickle from him severed the sinews of his hands and feet, and lifting him on his shoulders carried him through the sea to Cilicia and deposited him on arrival in the Corycian cave. Likewise he put away the sinews there also, hidden in a bearskin, and he set to guard them the she-dragon Delphyne, who was a half-bestial maiden. But Hermes and Aegipan stole the sinews and fitted him unobserved to Zeus. And having recovered his strength Zeus suddenly from heaven, riding in a chariot of winged horses, pelted Typhon with thunderbolts and pursued him to the mountain called Nysa, where the Fates beguiled the fugitive; for he tasted of the ephemeral fruits in the persuasion that he would be strengthened thereby.

So being again pursued he came to Thrace, and in fighting at Mount Haemus he heaved the whole mountains. But when these recoiled on him through the force of the thunderbolt, a stream of blood gushed out on the mountain, and they say from that circumstance the mountain was called Haemus. And when he started to flee through the Sicilian Sea, Zeus cast Mount Etna in Sicily upon him. That is a huge mountain, from which down to this day they say that blasts of fire issue from the thunderbolts that were thrown.
 

Harpers Dictionary of Classical Antiquities (1898)

Typhon (Tuphaôn) or Typhōeus (Tuphôeus). A monster of the primitive world, who is described sometimes as a destructive hurricane, and sometimes as a fire-breathing giant. According to Homer, he was concealed in the earth in the country of the Arimi, which was lashed by Zeus with flashes of lightning ( Il.ii. 782). In Hesiod, Typhon and Typhoeus are two distinct beings. Typhon is represented as a son of Typhoeus, and a fearful hurricane, and as having become by Echidna the father of the dog Orthus, Cerberus, the Lernaean hydra, Chimaera, and the Sphinx. Typhoeus, on the other hand, is called the youngest son of Tartarus and Gaea, or of Heré alone, because she was indignant at Zeus having given birth to Athené. He is described as a monster with 100 heads, fearful eyes, and terrible voices, who wanted to acquire the sovereignty of gods and men, but, after a fearful struggle, was subdued by Zeus with a thunderbolt. He begot the winds, whence he is also called the father of the Harpies; but the beneficent winds Notus, Boreas, Argestes, and Zephyrus were not his sons. He was buried in Tartarus, under Mount Aetna, the workshop of Hephaestus, whence it is called by the poets Typhoïs Aetna (Ovid, Fasti, iv. 491). Typhus was identified by the Greeks with the Egyptian god Set, who typified the power of darkness, and who slew Osiris.
 

Encyclopedia Mythica

Typhon is the offspring of Gaia and Tartarus. His mate is Echidna and both were so fearful that when the gods saw them they changed into animals and fled in terror. Typhon's hundred, horrible heads touched the stars, venom dripped from his evil eyes, and lava and red-hot stones poured from his gaping mouths. Hissing like a hundred snakes and roaring like a hundred lions, he tore up whole mountains and threw them at the gods.

Zeus soon regained his courage and turned, and when the other gods saw him taking his stand, they came back to help him fight the monster. A terrible battle raged, and hardly a living creature was left on Earth. But Zeus was fated to win, and as Typhon tore up huge Mount Aetna to hurl at the gods, Zeus struck it with a hundred well-aimed thunderbolts and the mountain fell back, pinning Typhon underneath. There the monster lies to this very day, belching fire, lava and smoke through the top of the mountain.

Echidna, his hideous mate, escaped destruction. She cowered in a cave, protecting Typhon's offspring, and Zeus let them live as a challenge to future heroes. Echidna and Typhon's children are the Nemean Lion, Cerberus, Ladon, the Chimera, the Sphinx, and the Hydra.
 

The Orphic Egg

From Bryant's An Analysis of Ancient Mythology
The ancient symbol of the Orphic Mysteries was the serpent-entwined egg, which signified Cosmos as encircled by the fiery Creative Spirit. The egg also represents the soul of the philosopher; the serpent, the Mysteries. At the time of initiation the shell is broken and man emerges from the embryonic state of physical existence wherein he had remained through the fetal period of philosophic regeneration.

The orphic egg is the inspiration for the Typhon logo.  Typhon was one of the many creatures that spawned from the egg.