Andrew Gelman has a great post about the concept of statistical significance, starting with a published definition by the Department of Health that is technically wrong on many levels. (link)
Statistical significance is one of the most important concepts in statistics. In recent years, there is a vocal group who claims this idea is misguided and/or useless. But what they are angry about is the use (and frequently, mis-use) of p-values, which is one way to measure statistical significance. In my view, this concept is never as important as it is today, in the world of Big Data.
Statistical significance codifies a core principle--that the observed dataset is not sufficient to answer your question (no matter how big the dataset is). It says that your observed sample is only one of many possibilities. If you could repeat your data collection, your dataset would look different. It might look just a slight bit different, or it might look vastly different. This "chance" that people keep talking about is merely the variations you get between one sample and another. By its very nature, this is a thought experiment -- you only have one observed sample.
But that is the point. Sound statistical reasoning requires you to think beyond your one observed sample.