The Phillips Curve represents the inverse relationship between the rate of inflation and unemployment, ceteris paribus.
|\
| \
Annual Rate | \
of Inflation | \
| \
| \
| \
+--------------
Real Unemployment Rate
Lower unemployment rates are related to higher rates of inflation. Although it should never be assumed that high inflation causes low unemployment or vice versa, but that, by observation, that is what happens.
Modern economists believe that the Phillips Curve is only accurate during the short-run. A good example is the boom of the 1990's in the US, where although there was very low unemployment, inflation was low too. That was because productivity growth was increasing at such a rate that it increased aggregate supply.
What's interesting though is that US economic policy is built around the Phillips curve. According to their thinking, it was impossible to achieve "full unemployment with out inflation" - fiscal and monetary policy could be used to find a place along the curve.
The curve is named after A.W. Phillips, a British economist who developed the idea.