Alongside stars, the galaxy is the most important unit of organization in the entire universe. There are an estimated 100 billion galaxies in the visible universe, each with between about ten million and a trillion stars. The average galaxy includes about 1071 atoms, and ten times more invisible mass in the form of dark matter. Galaxies themselves tend to be arranged into large structures called superclusters, which are in turn arranged into massive filaments separated by immense voids. The largest of these voids, the Eridanus Supervoid, has a diameter of nearly 1 billion light-years, about a 10,000 times wider than the Milky Way Galaxy.
Our own galaxy, the Milky Way, has between 200 and 400 billion stars, many of which are very faint due to exhausting their nuclear fuel long ago. To get a size of its scale, if 100 billion human beings could occupy the space around each star, then the entire Galaxy could provide space for roughly 1022 humans, more than the number of grains of sand on all of Earth's beaches. The galaxy is only about 100,000 light-years wide and 1,000 light-years thick.
This means that the entire galaxy could be colonized in only one million years, about four times the duration that the human species has existed, using starships traveling at 1% the speed of light. Most of the visible stars in the galaxy are main sequence stars, similar to our Sun. A minority are Red Giants, stars much larger than our Sun but very diffuse.
Though our galaxy is big -- 100,000 light-years across -- it is small enough that if expansion-oriented spacefaring civilizations had emerged in the first 99.9% or so of its history, they'd already be here by now. This is a strong argument for the absence of spacefaring extraterrestrial civilizations in our Galaxy. It is possible that such civilizations have emerged only extremely recently, but the a priori possibility of such a recent emergence is quite low, on the order of 1 in 10,000 or 1 in 100,000, if the probability of emergence is evenly distributed over much of the Galaxy's existence.
The Milky Way Galaxy is not a loner, but is actually a binary galactic system, gravitationally locked to our sister galaxy, the Andromeda Galaxy, about 2 million light-years away. Both our Galaxy and Andromeda are members of the Local Group, a collection of over 35 galaxies. The Milky Way is thought to be the most massive, though possibly the second largest, after Andromeda. The Local Group itself is embedded in the larger Virgo Supercluster, which contains over 100 galaxies within an area measuring 110 million light-years across.