We are living in a galaxy that we simply call “The Milky Way”. It is a middle sized spiral galaxy, or more precisely a barred spiral galaxy, with spiral arms and a kind of straight structure in the middle.
I cannot show you a picture of the Milky Way from the outside, since we are all living on the inside of it and we have not yet been able to send a space probe to the outside. But there are other galaxies that are of the same type, and they all look similar to the picture below (which actually is a computer rendering of our Milky Way).
The Milky Way have two distinct spiral arms, and a few additional, less bright and less clear arms or “spurs”. Our Sun lies near a small, partial arm called the Orion Spur, located between the Sagittarius and Perseus arm, in the “suburbs” so to speak. If the Milky Way was New York and the galactic center was Lower Manhattan, we would be living in Poughkeepsie.
The Milky Way is part of a small cluster of galaxies, called (perhaps not so imaginatively) “The Local Group”. The biggest galaxy in the neighborhood is the Andromeda Galaxy, which is in fact slightly bigger than our own. The Triangulum Galaxy is much smaller, and than there are a bunch of smaller, irregular dwarf galaxies.
As it happens, the Milky Way and the Andromeda Galaxy are on a collision course with each other, and are expected to collide in about 4.5 billion years.
This sounds more dramatic as it is - in fact, the galaxies contain so much empty space, that two galaxies can easily pass through each other without any stars actually colliding. Earth, or whatever is left if it, will probably not smash into something nasty. A stellar collision is less likely than two flies buzzing around in St. Peter’s Basilica colliding with each other in midair.
But the two galaxies will still eventually capture each other with their gravity and go through a series of oscillations to finally merge into one massive, distorted galaxy, like the two galaxies being in such a merge in the Hubble photo below.
Another cool fact is that in the heart of the Milky Way is a supermassive black hole, called Sagittarius A* (yes, it is actually pronounced a-star).
When this black hole was still young, it was still surrounded by gas clouds and stars. Having a black hole in this area was a bit like a placing a hungry tiger amidst a flock of sheep. It went into a feeding frenzy, devouring everything in its vicinity, growing for each swallowed star, belching out leftover matter and radiation that could not fit into its gaping throat at once. During this time, our galaxy was probably what astronomers call a “quasar”: the most luminous objects that ever existed, shining brightly as a beacon through the entire Universe.
Sgr A* however is now sleeping: it is dormant, dark and docile, having devoured everything in its vicinity a long time ago.
Frightening as a supermassive black hole in the center of our own galaxy might be, the Milky Way does not revolve around it. In spite of the black hole’s incredible mass, it dwarfs to insignificance when compared with the entire galaxy. Its gravitational effect on the galaxy is comparable with one of your eyelashes affecting your body with its mass.
So what holds the galaxy together? Why does it not fall apart? Given their incredibly fast rotation, galaxies should in fact fly apart into a thousand pieces, like a marshmallow attached to a lathe.
This is actually a very tricky question, and one that we still do not have a definite answer to.
We however believe that all galaxies are held together by something called “dark matter”. This is not just ordinary stuff that happens to be “black”, or “stuff that is in the shade”, but something fundamentally different. Dark matter does not interact with any electromagnetic force. You cannot shine a light onto it. It does not cast a shadow. It is in fact fully transparent. It is all around you as you read this, but you cannot observe it in any way. The only thing it has is gravity.
We today believe that dark matter is the most usual “stuff” in the entire Universe. And it does not get diluted as the Universe expands since it is most likely concentrated inside the galaxies, which do not get affected by cosmic expansion on a local level.