What relationship does Phillips curve show us?

Bill Phillips was an economist from New Zealand who spotted that when employment levels are high, wages rise faster, therefore people start spending more money, therefore, boosting aggregate demand. This evantually leads to to an increase in price levels - higher inflation. In the case of high unemployement, people have less money to spend, so price levels go down, respectively. 

Therefore, according to Phillips curve there is an inverse relationship between infaltion and unemployment. This trade-off can be also demonstrated on AD & AS diagram. In the period of economic growth, an increase in AD leads to higher Real GDP, we can assume that firms start to employ more workers and unemployment falls. However, as the economy gets closer to its full capacity we can expect an increase in infaltionary pressures. As with low unemployment workers will start demanding higher wages - wage inflation. Firms will start charging higher prices.