Statistically significant refers to something that is thought to have
sufficient evidence not to have occured by
chance. This is to say, we assume something to be statistically significant if the
likelihood of it having occured by chance is very low, hence the likelihood of occuring by
design is very high.
Usually, the critical value for statistical significance is p=<.05. This means that if we believe the probability of something having occured by chance is less than or equal to .05, we assume it has not occured by chance.
This critical value is not hard and fast, however. Depending on the issue being analyzed, the probability value may be .10, or lower, say .01, or .001.