You make assumptions about the nature of the distribution for a
set of observations and determine a pair of competing hypotheses -
a null hypotheis and an alternative. Based on the null hypothesis
you devise a test for a statistic that is based on the
observations. Assuming the null hypothesis is true, if the
probability of observing a test statistic that is at least as
extreme as the one obtained is smaller than some pre-determined
level (that is, if the observations are very unlikely under the
null hypothesis) then the result is said to be statistically
significant.
This does not automatically imply managerial significance since,
among other factors, the latter must take account of the
consequences (costs) of making the wrong decision.