When economists, um..."do" econometrics, they're doing rigorous statistical analysis, wading through gobs of data to try to find correlations. Unfortunately, econometrics can never give us a for-sure causal relationship, but economists do the best they can. By taking into account all relevant variables, they hope to find meaningful correlations that could be causations.
In econometrics, an endogenous variable is a variable that correlates with another variable. Like...the more you eat, the more your hunger, um...goes away, which means your hunger is an endogenous variable in that relationship. The farther you drive, the less gas you have in your tank. The hotter you get, the more you sweat. Endogenous variables are dependent, meaning they follow other variables.
On the flip side, we have exogenous variables: variables that don't give a hoot-and-a-half about what other variables are doing. They just do their own thang.
An economist's wildest hopes and dreams? To estimate the relationships between different variables using both endogenous and exogenous variables.