Let's further define mutation as a heritable change in the genetic material. This point becomes important in multicellular organisms where we must distinguish between changes in gametes (germline mutations) and changes in body cells (somatic mutations).
Statistical significance relates to the question of whether or not the results of a statistical test meets an accepted criterion level. In psychology this level is typically the value of p < .05. The criteria of p < .05 was chosen to minimize the possibility of a Type I error, finding a significant difference when one does not exist. It does not protect us from Type II error, failure to find a difference when the difference does exist.
What researchers mean by... statistical significance. It's easy for non-scientists to misunderstand the term significant when they come across it in an article. But when researchers say the findings of a study were statistically significant, they do not necessarily mean the findings are important.