We live in the Milky Way Galaxy, which is a collection of stars, gas, dust, and a supermassive black hole at it's very center. Our Galaxy is a spiral galaxy, which are rotating structures that are flat (disk-like) like a DVD when looked upon edge-on. There is also a bulge in the middle that consists of mostly old stars. When you look at a spiral galaxy face-on, you can see beautiful spiral arms where stars are being born. Our solar system is in the Orion arm, and we are about 25,000 light years (2.5 X 10^17 miles) from the very center of the Galaxy.
Since our solar system lies in one of the spiral arms, we live in the flat plane of the Milky Way. We can actually see the dense plane of the Milky Way stretch across the sky in dark places that do not have a lot of surrounding light pollution. The diffuse light is the combined light from millions of stars. Some of the light from these stars are obscured by large clouds of dust, which is why there are dark patches. Dust and gas are necessary to form stars, and most stars are formed within the spiral arms. Note that we can't really see the center of the galaxy with our eyes because there is dust in the way!
The very center of the Milky Way is known as the Galactic Center. It has a unique collection of very exotic objects that have intrigued astronomers for many decades. Some examples include a quiescent supermassive black hole, a collection of wispy magnetic filaments, a few dense stellar superclusters which host mysterious and massive stars, and a family of gas streamers spiraling toward a central dark mass.