Humans talk about the universe a lot, and sometimes it's strangely satisfying to start with our everyday intuitions and then see how far we can stretch them on the scale of the universe.
A bullet shot from a modern rifle travels at about 1200 m/s. Most people would agree that in the scope of things that humans interact with every day, this is pretty fast.
The international space station is traveling over six times the speed of our modern rifle bullet — about 7660 m/s. This is faster than anything humans have direct experience with on the earth. To put this into perspective, if the ISS flew past you at sea level it would take a little over a second for it to get from horizon to horizon. You wouldn't have much time to register that it was coming toward you (aside from the atmospheric havoc it would wreak, but we don't have to deal with that sort of thing in our pleasant thought experiment).
On September 5th, 1977, the Voyager 1 spacecraft was launched. It has been traveling for over 40 years, and is now beyond what most people consider to be the boundary of our solar system, well into the interstellar medium. As of this writing, it is about three times the distance from the sun as Pluto (Voyager Mission Status). Voyager 1 is currently traveling at about 17000 m/s relative to the sun, well over twice the orbital speed of the ISS. This is faster than most of our intuitions can grasp, but we're still on Earth's doorstep on a galactic scale.
The closest star to our solar system is Proxima Centauri, about 4.2 light years away. At the current stupendous speed of Voyager 1, it would take about 74,000 years to reach Proxima Centauri (if that's the way Voyager was headed, which it is not). 74,000 years encompasses just about all of the history of Homo Sapiens after we expanded out of Africa — a long time.
So now we've established that Proxima Centauri is really far away. The distance is 4.2 light years. The Milky Way galaxy, our own corner of the universe, is about 100,000 light years across. For Voyager to make that journey at its current speed would take about 1,763,500,000 years. That's a significant percentage of the age of the earth itself. We're now at distances that I cannot intuit at all.
The Milky Way is a part of a cluster of galaxies called the Local Group. We know that there are at least 54 galaxies in the Local Group, but the Milky Way partially occludes our view. Each of these galaxies contains millions to hundreds of billions of stars. Andromeda, about 2.5 million light years from Earth and one of the biggest galaxies in the local group, is estimated to contain a trillion stars. The entire Local Group of galaxies is about 10 million light-years across.
The Local Group is gravitationally bound to an even bigger structure, the Virgo Supercluster. Within the Virgo Supercluster are least 100 groups and clusters of galaxies, many of which are larger than the Local Group. The Virgo Supercluster is about 110 million light years across.
This ludicrous distance is dwarfed, however, by the size of the observable universe, which is estimated to be about 93 billion light years in diameter. It's estimated to contain about 10 million superclusters. This is absurdly, incomprehensibly large.
Thanks for stretching with me!