The Hubble expansion
During the 1920's and 30's, Edwin Hubble discovered that the Universe is expanding, with galaxies moving away from each other at a velocity given by an expression known as Hubble's Law: v = H*r. Here v represent's the galaxy's recessional velocity, r is its distance away from Earth, and H is a constant of proportionality called Hubble's constant.
The exact value of the Hubble constant is somewhat uncertain, but is generally believed to be between 50 and 100 kilometers per second for every megaparsec in distance, km/sec/Mpc. (A megaparsec is given by 1 Mpc = 3 x 10^6 light-years). This means that a galaxy 1 megaparsec away will be moving away from us at a speed of between 50 and 100 km/sec, while another galaxy 100 megaparsecs away will be receding at 100 times this speed. So essentially, the Hubble constant sets the rate at which the Universe is expanding.
Additionally, the present age of the Universe can be assessed vis-a-vis the Hubble constant: the inverse of the Hubble constant has units of time. By substituting in kilometers for Mpc in the Hubble constant, we find that upon inverting H we get a quantity with units of seconds (kilometers canceling out in the denominator and numerator). For a Hubble constant of 100 kilometers per second per Mpc, we get 3 x 10^7 seconds, or about 10 billion years. For H=50 kilometers per second per Mpc, the time scale is 20 billion years.