Econometrics literally means 'economic measurement'. It is the branch of economics that applies statistical methods to the empirical study of economic theories and relationships. It is a combination of mathematical economics, statistics, economic statistics and economic theory.
The two main purposes of econometrics are to give empirical content to economic theory and also to empirically verify economic theory. For example, econometrics could empirically verify if indeed a given demand curve slopes downward as economic theory would suggest. Empirical content is also given in that a numerical value would be given to this slope, while economic theory alone is usually mute on actual specific values.