Galactic things relate to a galaxy, a complex system of stars, especially the one in which we live. The very middle of our galaxy can be called the galactic center.
When something's described as galactic, it usually has something to do with astronomy. The adjective is good for talking about the characteristics of our galaxy, or specifying that something exists within our galaxy. Galactic can also be used informally to simply mean huge: "Did you see the size of their house? It's galactic!" The word, along with galaxy, comes from the Greek phrase galaxias kyklos, "milky circle."