Galaxies are vast concentrations of stars that we can see thoughout the universe. These gravitationally-bound collections of billions of stars are amoung the largest objects we can perceive.
Galaxies are classified by their shape. There are three distinct shapes, spiral, elliptical and irregular, with several variations within each classification.
We observe galaxies in every direction we look. The plane of the Milky Way contains vast tracks of dust which obscure of view of galaxies, so our best view is in directions away from that plane.
NASA's Hubble Space Telescope showed the depth and richness of the galactic population by producing an very special image, shown below. By staring at an area of the sky where we had previously observed nothing, and remaining focused on that area for a whole month, we were able to find that the further we look, the more galaxies we see.