A statistically significant difference is a difference that we think is not just due to chance. I say “think”, because we are never completely certain. We express how certain we are by the p value. A p value of 0.05 indicates a 5% uncertainty, or a 95% probability.
Ok so we think there is a difference, but is it an important difference? Maybe, maybe not. Statistics don’t tell us the answer to this question. We have to think about the degree of difference and what that might mean. For example would that difference change how you would treat an animal? Would it change the treatment you recommend? Would it change when something happens by an important amount? This is what we mean by clinical significance.
Just because there is statistically significant difference, it does not necessarily follow that the difference is clinically significant.