What is the Phillips curve?

In economics, the Phillips curve is the short-run tradeoff between the unemployment rate and inflation. The relationship implies a negative correlation such that an increase in the unemployment rate is associated with a decrease in wage rate. Conversely, during times in which the unemployment rate is quite low (strong demand for labor) the growth of wages is typically observed to be quite high, or increasing. While this phenomenon has been observed  in the short-run there are some periods in which the relationship does not hold.