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You get a number at the end which corresponds to numbers on a chart (I think?) and then you measure it against that and it gives you an empirical measurement of how similar two sets of variables are.
economics is GRAPHS. LOTS OF FACKIN' POINTLESS GRAPHS TO PROVES THINGS THAT ARE OBVIOUS.
associations between two sets of categorical variables, as lemonbrickcombo has said.
Let's say you're asking people whether they own a car or not. That's a categorical variable: yes or no.
You want to know if more people own cars who, let's say, went to uni or not. You take your responses and split them into those who did go to uni, and those who didn't (another categorical variable).
The chi-square analysis will calculate the pattern of responses that's to be expected if going to uni has no difference on car ownership (so that's proportionally equal responses across all the groups). It then compares them with the actual responses.
If the actual and expected responses do not match (and this matching process is determined by probability analysis), you'll get a significant chi-square analysis figure, and you can say with confidence that going to uni has SOME effect on car ownership. And then make further analyses to test exactly what these effects are.