It is actually the inside of the disc of the Milky Way Galaxy. We live in this disc. Light from stars in the disk is blurred by the gas or hidden by dust clouds in the disc.
The ancient astronomers called this streak the Milky Way. That is why our Galaxy is often called the Milky Way Galaxy.
How did the Milky Way Get its Name?Nobody is sure how the Milky Way got its strange name. The ancient Greeks had several stories about it. According to Cassell's Dictionary of Classical Mythology, Jenny March, 2001:
the mythological explanation for the origin of this smear was that the goddess Hera was tricked into suckling the baby Heracles, son of her husband Zeus by the beautiful mortal Alcmene. But when she discovered who the baby was she tore her breast from his mouth, and her milk spurted across the sky. You understand, of course, that the gods lived in the sky.
There was also another legend that the Milky Way was created when Phaethon, son of Helios (the Sun-god) set the heavens on fire with his father's sun-chariot.
Ovid in Metamorphoses 1.168-71 saw it as the highway of the gods, leading to Jupiters palace.