It is simply the intersection of the economics
sciences.Since the question "what the hell is econometrics?" makes
me wanna puke, let me write down some weird but intellectual stuff as my first entry.
In classical economics you are just taught the economical theorems, but the most considerable side of econometrics is that it gives you the chance to implement some numerical methods on these mentioned theorems through statistics and mathematics; thereby, talking through the language of maths, your interpretations about a certain economical issue would sound thoroughly objective. It is generally believed that the econometrical methods are severely hard to understand,but still it is quite useful in interpreting and obtaining consistent inferences from complex economical structures.
As a brief conclusion, econometrics is the numerical study of economical theorems through mathematics and statistics. To succeed in the study of econometrics, a well understanding of mathematics and probability is essential.
you gotta have the gut to apply for a phd in econometrics.