What is the significance of autocorrelation? Say that I have a signal that is strongly or weakly autocorrelated with itself. So what? What does this mean? How can this improve businesses? Does this mean that we can construct predictive models with time variables? 
I don't understand why autocorrelation is seen as a big deal or how it helps us shift focus. Why do people care about autocorrelation so much?
 A: Autocorrelation is a simple, reliable technique to find cyclic patterns in data.
If you have a one-hour-intervaled time series over let's say one week, you can create about 35 new time series (7 days in one week x 5 weeks) by lagging the original series by n days (n is from 1 to 35) by one day.
Next calculate R-squared for the original series and each lagged series; then plot those data points (n, or units of lag on the x-axis, and R-squared on the y-axis)
if instead of R-squared, you calculate correlation (so negative y values are possible) then plot those values, you get a correlogram and by looking at its shape it can tell you about the inter-day periodicity of that series. 
so for very high R-squared (near 1.0) the original series and lagged series are back in phase; if this occurs at multiples of seven, for instance, then your data has weekly periodicity.... 
there's a lot of reasons why this valuable information, not the least of which is that removing cycles (and the trend and regime shift if any) is a crucial predicate before forecasting (predicting future values in a time series). So for instance, perhaps the most frequently used family of forecasting models is ARIMA; the first two letters in that acronym stand for auto-regressive.
