|NGC 1097, a barred spiral galaxy, photo by NASA|
On a large scale, we live in an expanding universe: the galaxies are moving apart, with velocity proportional to distance. This is the cool part --- the galaxies are not moving through space, nor are the galaxies themselves expanding -- space itself is expanding, carrying the galaxies along!! Gravity within a galaxy holds it together. This does not mean we are at the center of the universe; you have the same impression of space expanding in all directions from any other galaxy as well. In local galaxy clusters, gravity can dominate over this expansion. Recessional velocities are greater than small local motions over large distances.
Knowing the current rate of expansion of the universe, we can estimate the time it took for galaxies to move as far apart as they are today: time = distance/velocity; velocity = (Hubble constant) distance. T = 1/H = about 14 billion years. You get same answer no matter which galaxy you pick. Looking back toward the early universe; the more distant the object we see, the further back into the past of the universe we are looking. Then we see dark zone where there are not galaxies. Then we see the cosmic microwave background radiation, the most distant light we can see. This radiation from very early phase of the universe should still be detectable today; discovered in mid-1960s s the Cosmic Microwave Background radiation, black body radiation with a temperature = 2.73 K.
Tomorrow: astronomy is a time machine, looking back into the past!