Econometrics uses stochastic methods with emphasis on applications; estimation, hypotheses testing, regression analysis, economic forecasting, time series analysis and probabilistic formulation of economic relationships such as consumption and production functions. In short econometrics uses a lot of stat and math to predict the economy.
Also to break it down even further, econometrics is used to quantify economic problems and find solutions. In other words, econometrics is used to answer the economic questions of "how much" and "how many". For example, suppose a popular advertisement shifts the demand curve to the right for a certain good. You could then use econometrics to measure by how much the demand curve has shifted.