A galaxy is a massive collection of stars gravitationally bound around a common central core. It is believed that most, if not all galaxies have at their core a super massive black hole - a black hole coming in at hundreds of thousands or billions times more massive than our own Sun.
Speaking of our own Sun, you can imagine a galaxy to be a super-sized solar system. Rather than a few planets orbiting a single star, a galaxy contains billions or hundreds of billions of stars orbiting a single or multiple black holes.
Galaxies come in different shapes. Most folks think of the classic spiral galaxy shape as shown in the spectacular image taken by the Hubble Space Telescope to the left, but galaxies can also be found in elliptical shapes ranging from nearly spherical to highly elongated and even ring shaped morphologies. Some lack much definable shape at all. This is usually due to “collisions” or interaction with neighboring galaxies.
Galaxies tend to cluster together in groups forming beautiful strands and webs throughout the universe. Our own local group contains 30 or more galaxies. Galaxies can also be incredibly big. The most recent observations of the Andromeda Galaxy, our nearest Spiral neighbor and largest member of our local group, put the count at some 1 trillion stars.
You might also be interested to know that the Andromeda Galaxy and the Milky Way Galaxy (the galaxy we call home) will someday merge into a giant elliptical galaxy. We are drawing towards each other at a pace around 60-90 miles per second. But with Andromeda almost 4.5 light years away, the merger isn’t expected to go through until sometime in 2.5 Billion AD. You might not want to bother waiting in line for good seats.