Some economic variables are determined by our models, while others are usually assumed to be determined by factors outside of our models. We call the former endogenous variables and the latter exogenous variables.
For econometric applications, the crucial difference between an endogenous and an exogenous variable is that we must assume that exogenous variables are not systematically affected by changes in the other variables of the model, especially by changes in the endogenous variables.
For example, if we are modeling the individual supply of corn produced in a year by Farmer Jones, the endogenous (or dependent) variable would probably be the amount of corn sold. This is the "output" of our economic model of Farmer Jones's production decision. The "inputs" would be the explanatory variables that influence the amount he sells, which might include the market price and the amount of rain that falls during the summer.
Can these inputs to the model be safely treated as exogenous variables? In this case, the answer is probably yes. Suppose that something (other than price or rainfall) were to cause Farmer Jones's production to be higher than normal (perhaps an unexpectedly good application of fertilizer). To decide whether the "input" variables are exogenous, we would have to determine whether this increase in production would cause them to change.
A rise in Jones's production will have no effect on the weather, so it seems safe to judge rainfall to be an exogenous variable. Corn prices could be a more difficult question. However, since Jones is only a microscopic part of the U.S. corn market, it seems likely that any imaginable increase in his production would have no discernable effect on the market price. Thus price can probably also be treated as exogenous.
To see how the exogeneity of an explanatory variables can be a difficult question, consider a closely related model: the supply of corn produced in a year by all the farmers in the state of Iowa. Once again, Iowa corn production would have no effect on the weather, so rainfall is clearly exogenous. However, if Iowa corn farmers increase their output significantly it is very likely to lower the U.S. price of corn. Thus, market price would be an endogenous variable in this model.
The presence of endogenous variables as explanatory variables in our economic models creates significant difficulties for estimating our model. For the present, we shall assume that all of the explanatory variables in our models can safely be considered exogenous.