It's not just some condescending buzzword. Something that is "statistically significant" has been shown definitatively to have been due to the cause of some variable contrast between a control group and a test group. Statistical significance is extremely important. Suppose you want to test the effectiveness of a medicine to reduce the likelihood of a heart attack. You design a controlled study of two groups of people. Group A takes the medicine, and Group B takes a placebo. Suppose that Group A has a lower rate of heart attacks than Group B. Is this due to chance, or the medicine? It would depend on the magnitude of the differing rates, the contrat of all other variables, and the population size of the study.
When dealing with issues requiring heavy use of probabilities, like gun control or crime rates, slight variations in results or swings both ways are expected - even when no variables are changing. And when other variables are also changing, the outcome may become more difficult to wade through to see the effect a variable of interest has on the test group. This where statistical significance becomes a useful tool for tracking the impact of changes.
Infact, statistical significance is the pirmary reason one discounts single or rare events when making policy decisions. Because just a few events cannot significantly change the statistical outcome of a population and thus the inspection of such events is deemed statistically insignificant.
This is your basic college statistics 101 type stuff. Look it up.
Or you could just keep quoting dead poets... 
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