A galaxy is a large collection of stars, planetary systems, gas nebulae, dust clouds, dark matter and other astronomical objects with a total mass of typically 10 to the 9th (Billion) up to 10 to the 13th (quadrillion) solar masses bound by gravity. Their diameter can be several hundred thousand light years (Wikipedia).
A spiral galaxy is said to be edge-on when it is highly tilted with respect to our line of sight and is therefore seen "sideways".
A special case of a galaxy that appears edge-on is our Milky Way. Due to Earth's position close to the galactic plane, the galaxy appears as a bright band in side view. Since the earth is part of our Milky Way, this band also extends across the entire firmament.