In principle, a statistically significant result (usually a difference) is a result that's not attributed to chance. More technically, it means that if the Null Hypothesis is true (which means there really is no difference), there's a low probability of getting a result that large or larger.

What does it mean to be statistically significantly different?

A statistically significant difference is simply one where the measurement system (including sample size, measurement scale, etc.) was capable of detecting a difference (with a defined level of reliability). Just because a difference is detectable, doesn't make it important, or unlikely.

How do you tell if a difference is statistically significant?

Determine your alpha level and look up the intersection of degrees of freedom and alpha in a statistics table. If the value is less than or equal to your calculated t-score, the result is statistically significant.