Galaxies are large aggregations of stars, planetary systems, gas clouds and other celestial bodies.
Almost all evidence suggests that all of Blake and Avon's exploits took place in the Milky Way, Earth's home galaxy. Avon implied that intergalactic travel was impossible without an intergalactic drive which the Federation at least had yet to develop, though work may have been in progress.
On the other hand, Travis once surmised that constant pursuit by the Federation had driven Blake 'into this galaxy' suggesting a wide degree of intergalactic travel taking place, but he appears to really be talking about a particular planetary system rather than a galaxy proper and this may be a slip of the tongue.
The Andromedan invaders appear to have originated from the galaxy M31 2.2 million light-years from Earth. They may have developed the intergalactic drive the Federation was working on.