The direction of objects in the sky is determined by two angles, declination and right ascension. If we imagine all the objects projected onto the surface of a sphere ("the celestial sphere") then these two angles are analogous to latitude and longitude, which determine position on the Earth's surface. The celestial sphere is divided into constellations ("con-stellations"), which are analogous to countries on the Earth. Constellations contain prominent groupings of stars such as the Great Bear (Ursa Major) or Orion; these stars may have no real dynamical connection with one another, in that their distances from us may differ enormously.
Within constellations, objects are labelled with a Greek letter [alpha, beta...] roughly according to their brightness, and for fainter objects, by a number 1, 2,... . Thus " 61 Cygni" means "Object number 61 in the constellation Cygnus (the swan)". Galaxies, and other objects of non-stellar appearance such as nebulae (gas clouds) within our own galaxy, have a separate nomenclauture: thus the closest galaxy to ours, in the constellation of Andromeda is "M31" -- the 31st object in the old catalogue of Messier -- or, alternatively, "NGC224" -- the 224th object in the New General Catalogue. In the catalogues all these objects are of course precisely located by their "map reference", that is, by their right ascension and declination.
Principles of Cosmology and Gravitation, Appendix A. By M.V. Berry, Institute of Physics Publishing, Bristol and Philadelphia, 1993.
In a nutshell, if you are a user of the popular "Thomas Guides" available, at the very least, here on the west coast of the USA, when you go to find out where Buttonwillow, California, is, you look up in your Thomas Guide the page and grid location -- say, 224 E-5 -- and flip to page 224 and look where the rows and columns E and 5 intersect. Now you know where Buttonwillow is. If you were looking for the Lesser Magellenic Cloud, you'd look in your New General Catalogue to find the right ascension and declination, after which point you could identify the LMC on any photo that has right ascension and declination marked on it. Row, column, intersect on the pretty picture.
Just be glad the next Shell station isn't "one galaxy over".