Milky Way
The Milky Way is the barred spiral galaxy that contains our solar system, about 100,000 light-years across with a few hundred billion stars.
Definition
The Milky Way is the galaxy we live in, a flat spinning disk with spiral arms whose hundreds of billions of stars include our Sun; from Earth it appears as a hazy band of light across the night sky. It is a barred spiral about $100{,}000$ light-years in diameter, with the Sun sitting in a spiral arm about $26{,}000$ light-years from the center and a supermassive black hole, Sagittarius A*, at the core. In more detail, it is an SBbc-type galaxy with a central bulge, thin and thick disks, a stellar halo, and a dark matter halo extending far beyond the visible disk, and its total mass is on the order of $10^{12}$ solar masses, most of it dark. Sagittarius A* has about $4$ million solar masses, measured from the orbits of nearby stars.
Example
Far from city lights on a clear summer night, the Milky Way stretches across the sky as a milky stripe, the combined light of countless stars in the galaxy's disk. The Sun orbits the galactic center at about $220\ \text{km/s}$, completing one orbit in roughly $230$ million years, so it has made about $20$ trips since it formed. The star S2 orbits Sagittarius A* every $16$ years and comes within about $120\ \text{AU}$ of it, and applying Kepler's third law to that orbit gives the black hole's mass directly.
Key Insight
No photo of the whole Milky Way from outside exists, because we are inside it; full spiral views are drawings based on measurements. The milky band is the disk seen edge-on from within, and looking away from the band means looking out of the thin disk into deeper space with fewer stars. Nearly everything heavier than helium in your body was forged inside earlier generations of Milky Way stars and scattered by their deaths, which makes the galaxy a chemical recycling system and the Sun a later-generation product of it.